Measuring transducer of the vibration type as well as measuring system formed therewith

ABSTRACT

A measuring transducer comprises: a housing, with an inlet-side flow divider having four flow openings, and an outlet-side end having four flow openings; a tube arrangement having four tubes connected to the flow dividers; and a first coupling element. An exciter mechanism for producing and/or maintaining mechanical oscillations of the four measuring tubes. The first coupling element includes a deformation body and four connecting struts, of which connected with a first strut end and with the first measuring tube, a second connecting strut is connected with a first strut end and with a second strut end with the second measuring tube, a third connecting strut and with a second strut end with the first measuring tube, and a fourth connecting strut is connected with a first strut end and with a second strut end with the fourth measuring tube.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a Nonprovisional which claims the benefit of U.S. Application Provisional Application 61/428,541 which was filed on Dec. 30, 2010.

TECHNICAL FIELD

The invention relates to a measuring transducer of the vibration type for measuring a flowable medium conveyed in a pipeline, especially a gas, a liquid, a powder or another flowable material, especially a measuring transducer of the vibration type for measuring a density and/or a mass flow rate, especially also a total mass flow totaled over a time interval of a medium flowing in a pipeline at least at times having a mass flow rate of more than 1000 t/h, especially more than 1500 t/h. Additionally, the invention relates to a measuring system with such a measuring transducer, for instance, one embodied as an In-line measuring device.

BACKGROUND DISCUSSION

In process measurements and automation technology, for measuring physical parameters, such as, for example, the mass flow, the density and/or the viscosity of media flowing in pipelines—for instance, an aqueous liquid, a gas, a liquid-gas mixture, steam, oil, a paste, a slurry or another flowable material—such In-line measuring devices are often used, which, by means of a measuring transducer of the vibration type through which medium flows, and by means of a measuring and operating circuit connected thereto, effect reaction forces in the medium—such as, for example, Coriolis forces corresponding with a mass flow, inertial forces corresponding with a density of the medium and/or frictional forces corresponding with a viscosity of the medium, etc.—and, derived from these, produce a measurement signal representing the particular mass flow, viscosity and/or density of the medium. Such measuring transducers, especially measuring transducers embodied as Coriolis mass flow meters or Coriolis mass flow/densimeters, are described at length and in detail in, for example, EP-A 1 001 254, EP-A 553 939, U.S. Pat. No. 4,793,191, US-A 2002/0157479, US-A 2006/0150750, US-A 2007/0151368, U.S. Pat. No. 5,370,002, U.S. Pat. No. 5,796,011, U.S. Pat. No. 6,308,580, U.S. Pat. No. 6,415,668, U.S. Pat. No. 6,711,958, U.S. Pat. No. 6,920,798, U.S. Pat. No. 7,134,347, U.S. Pat. No. 7,392,709, or WO-A 03/027616.

Each of the measuring transducers includes a transducer housing, an inlet-side, first housing end of which is formed at least partially by means of a first flow divider having exactly two, mutually spaced apart, circularly cylindrical or tapered or conical flow openings, and an outlet-side, second housing end is formed at least partially by means of a second flow divider having exactly two, mutually spaced apart flow openings. In the case of some of the measuring transducers illustrated in U.S. Pat. No. 5,796,011, U.S. Pat. No. 7,350,421, or US-A 2007/0151368, the transducer housing comprises a rather thick-walled, circularly cylindrical, tubular segment, which forms at least a middle segment of the transducer housing.

For guiding a medium—in given cases also an extremely hot medium—which at least at times flows, the measuring transducers furthermore in each case include exactly two measuring tubes made of metal, especially steel or titanium, which are connected in such a manner that the medium can flow in parallel, and which are positioned within the transducer housing and held oscillatably therein by means of the aforementioned flow dividers. A first of the measuring tubes, which are most often equally constructed and extend parallelly relative to one another, opens with an inlet-side, first measuring tube end into a first flow opening of the inlet-side, first flow divider, and opens with an outlet-side, second measuring tube end into a first flow opening of the outlet-side, second flow divider. A second of the measuring tubes opens with an inlet-side, first measuring tube end into a second flow opening of the first flow divider, and opens with an outlet-side, second measuring tube end into a second flow opening of the second flow divider. Each of the flow dividers additionally in each case includes a flange with a sealing surface for fluid-tight connecting of the measuring transducer to tubular segments of the pipeline, which serve for supplying and removing medium to and from the measuring transducer, respectively.

For producing the reaction forces discussed above, the measuring tubes are caused to vibrate during operation, driven by an exciter mechanism serving for producing or maintaining, as the case may be, mechanical oscillations, especially bending oscillations, of the measuring tubes in the so-called wanted mode. The oscillations in the wanted mode are, especially in the case of application of the measuring transducer as a Coriolis mass flow meter and/or densimeter, most often formed at least partially as lateral bending oscillations, and, in the case of medium flowing through the measuring tubes, as a result of Coriolis forces induced therein, formed as additional, equal-frequency oscillations superimposed in the so-called Coriolis mode. Accordingly, the—here most often electrodynamic—exciter mechanism is embodied in such a manner, that, therewith, the two measuring tubes are, in the wanted mode, differentially—thus via introduction of exciter forces acting simultaneously along a shared line of action, but in opposed directions—excitable at least partially and especially also predominantly to opposite-equal bending oscillations.

For registering vibrations, especially bending oscillations, of the measuring tubes excited by means of the exciter mechanism, and for producing oscillation signals representing vibrations, the measuring transducers additionally in each case have a—most often likewise electrodynamic—sensor arrangement reacting to relative movements of the measuring tubes. Typically, the sensor arrangement is formed by means of an inlet-side oscillation sensor registering oscillations of the measuring tubes differentially—thus only relative movements of the measuring tubes—as well as by means of an outlet-side oscillation sensor registering oscillations of the measuring tubes differentially. Each of the oscillation sensors, which are usually equally constructed with respect to one another, is formed by means of a permanent magnet held on the first measuring tube and a cylindrical coil held on the second measuring tube and permeated by the magnetic field of the permanent magnet.

In operation, the above described tube arrangement formed by means of the two measuring tubes is at least excited by means of the electromechanical exciter mechanism to at times perform mechanical oscillations in the wanted mode at least one dominating, wanted oscillation frequency. In such case, usually a natural, instantaneous resonance frequency of the tube arrangement, which, in turn, depends essentially both on the size, shape and material of the measuring tubes as well as also on an instantaneous density of the medium, is selected as the oscillation frequency for the oscillations in the wanted mode; in given cases, this wanted oscillation frequency can also be influenced significantly by an instantaneous viscosity of the medium. As a result of fluctuating density of the medium being measured and/or as a result of media change occurring during operation, the wanted oscillation frequency during operation of the measuring transducer varies naturally, at least within a calibrated—and thus predetermined—wanted frequency band, which correspondingly has a predetermined lower limit frequency and a predetermined upper limit frequency.

For defining a wanted oscillatory length of the measuring tubes and, in association therewith, for adjusting the band of the wanted frequency, measuring transducers of the above described type additionally most often include at least one inlet-side coupling element, which is affixed to both measuring tubes and spaced apart from the two flow dividers, this coupling element serving for forming inlet-side oscillation nodes for opposite-equal vibrations—especially bending oscillations—of both measuring tubes, as well as at least one outlet-side coupling element, which is affixed to both measuring tubes and spaced apart both from the two flow dividers, as well as also from the inlet-side coupling element, this outlet-side coupling element serving for forming outlet-side oscillation nodes for opposite-equal vibrations—especially bending oscillations—of the measuring tubes. In the case of curved measuring tubes, in such case, the length of a section of a deflection curve of any of the measuring tubes extending between the inlet side and the outlet-side coupling elements—and consequently the length of an imaginary center line of said measuring tube connecting the areal centers of gravity of all imaginary cross sectional areas of the respective measuring tube—corresponds to the wanted oscillatory length of the measuring tubes. By means of the coupling elements, which thus belong to the tube arrangement, also an oscillation quality factor of the tube arrangement, as well as also the sensitivity of the measuring transducer, can additionally be influenced, in a manner such that, for a minimum required sensitivity of the measuring transducer, at least one minimum, wanted oscillatory length is provided.

Development in the field of measuring transducers of vibration type has, by this point, reached a level wherein modern measuring transducers of the described type can, for a broad application spectrum of flow measurement technology, satisfy the highest requirements as regards precision and reproducibility of measurement results. Thus, such measuring transducers are, in practice, used for mass flow rates from some few g/h (grams per hour) up to some t/min (tons per minute), at pressures of up to 100 bar for liquids or even over 300 bar for gases. The accuracy of measurement achieved, in such case, usually lies at about 99.9% of the actual value or above, or at a measuring error of about 0.1%, wherein a lower limit of the guaranteed measurement range can quite easily lie at about 1% of the measurement range end value. Due to their wide range of possibilities for use, industrial grade measuring transducers of vibration type are available with nominal diameters (corresponding to the caliber of the pipeline to be connected to the measuring transducer, or to the caliber of the measuring transducer measured at the connecting flange), which lie in a nominal diameter range of between 1 mm and 250 mm, and at maximum nominal mass flow rate of 1000 t/h, are in each case specified for pressure losses of less than 3 bar. A caliber of the measuring tubes lies, in such case, for instance, in a range of between 80 mm and 100 mm.

In spite of the fact that, by this point, measuring transducers for use in pipelines with very high mass flow rates and, in association therewith, very large calibers of far beyond 100 mm have become available, there is still considerable interest in obtaining measuring transducers of high precision and low pressure loss also for still larger pipeline calibers of about 300 mm or more, or mass flow rates of 1500 t/h or more, for instance for applications in the petrochemical industry or in the field of transport and transfer of petroleum, natural gas, fuels, etc. This leads, in the case of correspondingly scaled enlarging of the already established measuring transducer designs known from the state of the art, especially from EP-A 1 001 254, EP-A 553 939, U.S. Pat. No. 4,793,191, US-A 2002/0157479, US-A 2007/0151368, U.S. Pat. No. 5,370,002, U.S. Pat. No. 5,796,011, U.S. Pat. No. 6,308,580, U.S. Pat. No. 6,711,958, U.S. Pat. No. 7,134,347, U.S. Pat. No. 7,350,421, or WO-A 03/027616, to the fact that the geometric dimensions would be exorbitantly large, especially the installed length corresponding to a distance between the sealing surfaces of both flanges and, in the case of curved measuring tubes, a maximum lateral extension of the measuring transducer, especially dimensions for the desired oscillation characteristics, the required load-bearing ability, as well as the maximum allowed pressure loss. Along with that, also the empty mass of the measuring transducer increases unavoidably, with conventional measuring transducers of large nominal diameters already having an empty mass of about 400 kg. Investigations, which have been carried out for measuring transducers with two bent measuring tubes constructed, for instance, according to U.S. Pat. No. 7,350,421 or U.S. Pat. No. 5,796,011 as regards their to-scale enlargement to still greater nominal diameters, have, for example, shown that, for nominal diameters of more than 300 mm, the empty mass of a conventional measuring transducer enlarged to scale would lie far above 500 kg, accompanied by an installed length of more than 3000 mm, and a maximum lateral extension of more than 1000 mm. As a result, it can be said that industrial grade, mass producible measuring transducers of conventional design and materials with nominal diameters far above 300 mm cannot be expected in the foreseeable future both for reasons of technical implementability, as well as also due to economic considerations.

Taking this into consideration, in Endress Hauser's own, non-pre-published international patent applications PCT/EP2010/068251, or PCT/EP2010/068250, for example, new measuring transducers of vibration type, which are not least of all also scalable to comparatively large nominal diameters of more than 300 mm, are in each case provided, wherein the particular tube arrangement of these measuring transducers in each case comprises four bent measuring tubes—for example, at least sectionally V-shaped and/or at least sectionally circular arc shaped measuring tubes—for conveying flowing medium. These measuring tubes are in each case connected so as to form flow paths which are flow technologically connected in parallel to the flow dividers, which accordingly also each have four flow openings. Of the measuring tubes, a first measuring tube opens with an inlet-side first measuring tube end into in a first flow opening of the first flow divider, and opens with an outlet-side second measuring tube end into a first flow opening of the second flow divider; a second measuring tube parallel to the first measuring tube opens with an inlet-side first measuring tube end into a second flow opening of the first flow divider, and with an outlet-side second measuring tube end into a second flow opening of the second flow divider; a third measuring tube opens with an inlet-side first measuring tube end into a third flow opening of the first flow divider, and with an outlet-side second measuring tube end into a third flow opening of the second flow divider; and a fourth measuring tube parallel to the third measuring tube opens with an inlet-side first measuring tube end into a fourth flow opening of the first flow divider, and with an outlet-side second measuring tube end into a fourth flow opening of the second flow divider. In an interesting aspect, in PCT/EP2010/068251, not least of all for the purpose of reducing undesired oscillation-related deformations of the flow dividers, it is additionally provided to excite as the wanted mode a natural bending oscillation mode inherent to the tube arrangement—the so-called V-mode—in which the first and second measuring tubes in each case execute opposite-equal bending oscillations about a static resting position associated with the respective measuring tubes, and in which the third and fourth measuring tubes in each case execute opposite-equal bending oscillations about a static resting position associated with the respective measuring tubes, and in such a manner that, relative to a imaginary longitudinal section plane of the tube arrangement extending between the first and third measuring tubes as well as also between the second and fourth measuring tubes, said bending oscillations of the first measuring tube are also opposite-equal to said bending oscillations of the third measuring tube, and that, relative to the imaginary longitudinal section plane, said bending oscillations of the second measuring tube are also opposite-equal to said bending oscillations of the fourth measuring tube.

Further investigations have revealed, however, that a special problem in such case can be that an eigenfrequency of said V-mode of the tube arrangement is initially—thus without taking additional actions—essentially equal to an eigenfrequency of an additional natural bending oscillation mode inherent to the tube arrangement—the so-called X-mode—in which the first and second measuring tubes in each case execute opposite-equal bending oscillations about a static resting position associated with the respective measuring tubes, and in which the third and fourth measuring tubes in each case execute opposite-equal bending oscillations about a static resting position associated with the respective measuring tubes, but do so, however, in such a manner that, relative to the aforementioned imaginary longitudinal section plane, said bending oscillations of the first measuring tube are also opposite-equal to said bending oscillations of the fourth measuring tube, and that, relative to the imaginary longitudinal section plane, said bending oscillations of the second measuring tube are also opposite-equal to said bending oscillations of the third measuring tube. As a result of this, in the case of measuring transducers with a tube arrangement of the aforementioned type having four measuring tubes, the case can certainly occur, that the tube arrangement, when actually exciting the V-mode, namely to its eigenfrequency, switches in an unpredictable manner from the V-mode to the X-mode and vice versa, or simultaneously oscillates both in the V-mode as well as also in the X-mode, so that the tube arrangement, as a result, at times assumes undefined oscillatory states.

SUMMARY OF THE INVENTION

Proceeding from the aforementioned state of the art, an object of the invention is consequently to provide a measuring transducer with a tube arrangement having four curved measuring tubes, wherein this tube arrangement also has a stable oscillatory state in the V-mode, and consequently wherein a use of at least the V-mode as the actively excited wanted mode is enabled, or a capability of said V-mode being used as an actively excited wanted mode is further improved.

For achieving the object, the invention resides in a measuring transducer of vibration type for registering at least one physical, measured variable of a flowable medium conveyed in a pipeline, for example, a gas, a liquid, a powder or other flowable material, and/or for producing Coriolis forces serving for registering a mass flow rate of a flowable medium conveyed in a pipeline, especially a gas, a liquid, a powder or other flowable material. According to the invention, the measuring transducer comprises a transducer housing—for example, an at least partially essentially tubular and/or at least partially externally circularly cylindrical transducer housing—an inlet-side, first housing end of which is formed by means of an inlet-side, first flow divider having exactly four flow openings, which are, for example, circularly cylindrical, tapered or conical, and which are in each case spaced apart from one another; and an outlet-side, second housing end is formed by means of an outlet-side, second flow divider having exactly four flow openings, which are, for example, circularly cylindrical, tapered or conical, and which are in each case spaced apart from one another. Furthermore, the measuring transducer comprises a tube arrangement with exactly four curved or bent (for example, at least sectionally V-shaped and/or at least sectionally circular arc-shaped) measuring tubes for conveying flowing medium, wherein these measuring tubes are connected, forming flow paths which are connected in parallel, to the flow dividers, which are, for example, constructed equally t one another. These measuring tubes are especially held oscillatably in the transducer housing solely by means of said flow dividers and/or are equally constructed and/or pairwise parallel relative to one another. Of the four measuring tubes, which are, for example, constructed equally both as regards geometry as well as also as regards material, a first measuring tube, especially a circularly cylindrical first measuring tube, opens with an inlet-side, first measuring tube end into a first flow opening of the first flow divider, and opens with an outlet-side, second measuring tube end into a first flow opening of the second flow divider; a second measuring tube, which is at least sectionally parallel to the first measuring tube, opens with an inlet-side, first measuring tube end into a second flow opening of the first flow divider, and opens with an outlet-side, second measuring tube end into a second flow opening of the second flow divider; a third measuring tube opens with an inlet-side, first measuring tube end into a third flow opening of the first flow divider, and opens with an outlet-side, second measuring tube end into a third flow opening of the second flow divider; and a fourth measuring tube, which is at least sectionally parallel to the third measuring tube, opens with an inlet-side, first measuring tube end into a fourth flow opening of the first flow divider, and opens with an outlet-side, second measuring tube end into a fourth flow opening of the second flow divider. Additionally, the measuring transducer comprises an electromechanical exciter mechanism—for example, one formed by means of one or more electrodynamic oscillation exciters—for producing and/or maintaining mechanical oscillations, for example bending oscillations of the four measuring tubes. In the case of the measuring transducer of the invention, the two flow dividers are additionally embodied and arranged in the measuring transducer in such a manner, that an imaginary first connecting axis of the measuring transducer imaginarily connecting the first flow opening of the first flow divider with the first flow opening of the second flow divider extends parallel to an imaginary second connecting axis of the measuring transducer imaginarily connecting the second flow opening of the first flow divider with the second flow opening of the second flow divider, and that an imaginary third connecting axis of the measuring transducer imaginarily connecting the third flow opening of the first flow divider with the third flow opening of the second flow divider extends parallel to an imaginary fourth connecting axis of the measuring transducer imaginarily connecting the fourth flow opening of the first flow divider with the fourth flow opening of the second flow divider, and the measuring tubes are embodied and arranged in such a manner, that the tube arrangement has a first imaginary longitudinal section plane extending both between the first measuring tube and the third measuring tube as well as also between the second measuring tube and the fourth measuring tube, and that the tube arrangement has a second imaginary longitudinal section plane, which is perpendicular to its imaginary first longitudinal section plane, and which extends both between the first measuring tube and second measuring tube as well as also between the third measuring tube and fourth measuring tube. Apart from this, the tube arrangement also additionally has an imaginary cross sectional plane, which is in each case perpendicular both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane. Furthermore, the tube arrangement, and consequently the measuring transducer of the invention formed therewith, comprises a first coupling element of a first type, which is spaced apart both from the first flow divider as well as also from the second flow divider; which is affixed, for example on the inlet side, on each of the four measuring tubes; which is, for instance, embodied as a frame construction and/or as an interconnection of struts; and which serves for setting the eigenfrequencies of natural oscillation modes of the tube arrangement, not least of all also such, in which measuring tubes in each case simultaneously execute or can execute bending oscillations about a particular static resting position. The first coupling element of the first type includes a deformation body, for example, one which is box-shaped and/or formed by means of a frame construction having a plurality of profile struts and/or plates, as well as four connecting struts, which, for example, are equally long and/or at least pairwise equally constructed, of which a first connecting strut, for example, a rod- or plate-shaped first connecting strut, is connected with a first strut end with the deformation body, and is connected with a second strut end with the first measuring tube; a second connecting strut, for example, a rod- or plate-shaped second connecting strut, is connected with a first strut end with the deformation body, and with a second strut end with the second measuring tube; a third connecting strut, for example, a rod- or plate-shaped third connecting strut, is connected with a first strut end with the deformation body and with a second strut end with the first measuring tube; and a fourth connecting strut, for example, a rod- or plate-shaped fourth connecting strut, is connected with a first strut end with the deformation body and with a second strut end with the fourth measuring tube.

Moreover, the invention resides in a measuring system for measuring density and/or mass flow rate—thus, for example, a total mass flow totalled over a time interval—of a medium flowing at least at times in a pipeline, for instance, a medium such as a gaseous material, a liquid, a powder or other flowable material, with, for example, a mass flow rate of more than 1000 t/h. The measuring system, for example one embodied as an In-line measuring device and/or a measuring device in compact construction, comprises said measuring transducer, as well as—electrically coupled with the measuring transducer, and, for example, arranged in an electronics housing mechanically connected with the transducer housing—a transmitter-electronics for activating the measuring transducer, especially its exciter mechanism, and for evaluating oscillation signals delivered by the measuring transducer. The invention especially thus resides in the use of said measuring system for measuring a density and/or a mass flow rate, especially a total mass flow totalled over a time interval, and/or a viscosity and/or a Reynolds number of a medium flowing in a process line, for instance, a pipeline at least at times with a mass flow rate of more than 1000 t/h, for example, of more than 1500 t/h; for instance, a medium such as, for example, a gaseous material, a liquid, a powder or other flowable material.

According to a first embodiment of the measuring transducer of the invention, it is additionally provided that the tube arrangement is mirror symmetrical relative to the first imaginary longitudinal section plane.

According to a second embodiment of the measuring transducer of the invention, it is additionally provided that the tube arrangement is mirror symmetrical relative to the second imaginary longitudinal section plane.

According to a third embodiment of the measuring transducer of the invention, it is additionally provided that the tube arrangement is mirror symmetrical both relative to the first imaginary longitudinal section plane as well as also relative to the second imaginary longitudinal section plane.

According to a fourth embodiment of the measuring transducer of the invention, it is additionally provided that the coupling element of the first type is embodied and arranged in such a manner, that it is mirror symmetrical both relative to the first imaginary longitudinal section plane as well as also relative to the second imaginary longitudinal section plane the tube arrangement.

According to a fifth embodiment of the measuring transducer of the invention, it is additionally provided that each of the four measuring tubes in each case has a bending stiffness determined by a modulus of elasticity dependent on a material of said measuring tube, as well as also by an areal moment of inertia dependant on a caliber and a wall thickness, and wherein both the second measuring tube as well as also the third measuring tube and the fourth measuring tube in each case have a bending stiffness, which, in each case, is equal to the bending stiffness, E₁₈·J₁₈, of the first measuring tube.

According to a sixth embodiment of the measuring transducer of the invention, it is additionally provided that the deformation body is formed by means of a frame construction, especially a frame construction having a plurality of profile struts and/or plates.

According to a seventh embodiment of the measuring transducer of the invention, it is additionally provided that inherent to the coupling element of the first type is an eigenmode of a first type, in which the deformation body of said coupling element can execute mechanical oscillations with an eigenfrequency in a plane of oscillation parallel to the imaginary cross sectional plane, wherein these oscillations are mirror symmetrical both relative to the first imaginary longitudinal section plane as well as also relative to the second imaginary longitudinal section plane, or which cause the deformation body to appear symmetrical both relative to the first imaginary longitudinal section plane as well as also relative to the second imaginary longitudinal section plane mirror, and also an eigenmode of a second type, in which the deformation body of said coupling element can execute mechanical oscillations in said plane of oscillation parallel to the imaginary cross sectional plane with an eigenfrequency which is, for example, also different from the eigenfrequency of the eigenmode of the first type, wherein these oscillations are mirror symmetrical only relative to the second imaginary longitudinal section plane, or the deformation body is temporarily caused to appear mirror symmetrical only relative to the second imaginary longitudinal section plane, and that the deformation body of the coupling element of the first type is embodied in such a manner, that an eigenfrequency ratio inherent to said coupling element, which is defined by a ratio of the eigenfrequency of its eigenmode of the first type to the eigenfrequency of its eigenmode of the second type, is greater than one, especially greater than 10.

Developing this embodiment of the invention further, it is additionally provided that inherent in the coupling element of the first type is a natural oscillatory mode of a third type, in which the deformation body, for example, only moving translationally in the direction of a longitudinal axis parallel both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane, can oscillate with an eigenfrequency about an associated static rest position, and in such a manner, that simultaneous to this, the four connecting struts execute—especially in the same direction and/or uniformly—bending oscillations about a particular static resting position, in the direction of the longitudinal axis, and that the coupling element of the first type is embodied in such a manner, that the eigenfrequency of its eigenmode of the third type is not equal to a measurable eigenfrequency of the bending oscillation mode of the first type of the tube arrangement in the case of measuring tubes completely filled with air, and is embodied, for example, in such a manner, that said eigenfrequency of the oscillatory mode of the third type of the coupling element of the first type is more than 10 Hz greater than said eigenfrequency of the bending oscillation mode of the first type of the tube arrangement, and/or that said eigenfrequency of the oscillatory mode of the third type of the coupling element of first type amounts to more than 101%, especially more than 105%, of said eigenfrequency of the bending oscillation mode of the first type of the tube arrangement.

Developing this embodiment of the invention further, it is additionally provided that inherent in the coupling element of the first type is a natural oscillatory mode of a fourth type, in which the deformation body, moving only translationally in the plane of oscillation parallel to the imaginary cross sectional plane, can oscillate with an eigenfrequency about its associated static rest position, and in such a manner, that the four connecting struts execute—for example, in the same direction and/or uniformly—bending oscillations around its particular static resting position in the coupler plane, and that the coupling element of the first type is embodied in such a manner, that the eigenfrequency of its eigenmode of the fourth type is higher than the measurable eigenfrequency of the bending oscillation mode of the second of type the tube arrangement in the case of measuring tubes completely filled with air, and embodied, for example, in such a manner, that said eigenfrequency of the mode of oscillation of the fourth type of the coupling element of the first type is more than 10 Hz greater than said eigenfrequency of the bending oscillation mode of the second type of the tube arrangement, and/or that said eigenfrequency of the mode of oscillation of fourth type of the coupling element of first type amounts to more than 101%, especially more than 105%, of said eigenfrequency, f_(18X), of the bending oscillation mode of the second type of the tube arrangement.

According to an eighth embodiment of the measuring transducer of the invention, it is additionally provided that the deformation body has at least two longitudinal struts—for example, equally constructed and/or plate-shaped longitudinal struts—of which a first longitudinal strut, which is, for example, at least sectionally straight, and which extends from the first connecting strut to the third connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, exclusively on a side of said longitudinal section plane occupied both by the first as well as also by the third measuring tube, and a second longitudinal strut, which is, for example, at least sectionally straight, and which extends from the second connecting strut to the fourth connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, for example by the same distance as the first longitudinal strut, exclusively on a side of said longitudinal section plane occupied both by the second as well as also by the fourth measuring tube. The two longitudinal struts, which especially are equally constructed, can be formed, for example, by means of a flat rod, especially one composed of metal, or can each be composed of the same material, and/or each be composed of steel.

Developing this embodiment of the invention further, it is additionally provided that the first longitudinal strut is at least sectionally straight—for example, predominantly or completely straight—in projection on the imaginary cross sectional plane, wherein the second longitudinal strut is at least sectionally straight—for example, predominantly or completely straight—in projection on the imaginary cross sectional plane; and/or that the first longitudinal strut at least sectionally extends perpendicular to the first imaginary longitudinal section plane, and consequently parallel to the second imaginary longitudinal section plane, wherein the second longitudinal strut at least sectionally extends perpendicular to the first imaginary longitudinal section plane, and consequently parallel to the second imaginary longitudinal section plane.

Alternatively or in supplementation of this, it is additionally provided that the first longitudinal strut has a minimal bending stiffness determined by a modulus of elasticity dependent on a material of said longitudinal strut, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to said longitudinal strut, and the second longitudinal strut has a minimal bending stiffness, determined by a modulus of elasticity dependent on a material of said longitudinal strut, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to said longitudinal strut, and that the first longitudinal strut and the second longitudinal strut are arranged in such a manner, that both the imaginary bending principal axis of the minimal areal moment of inertia of the first longitudinal strut as well as also the imaginary bending principal axis of the minimal areal moment of inertia of the second longitudinal strut in each case extend parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane. The first longitudinal strut and the second longitudinal strut are especially additionally embodied and arranged in such a manner, that the minimal bending stiffness of the first longitudinal strut is equal to the minimum bending stiffness of the second longitudinal strut.

According to a ninth embodiment of the measuring transducer of the invention, it is additionally provided that the deformation body has at least two longitudinal struts—for example, equally constructed and/or plate-shaped longitudinal struts—of which a first longitudinal strut, which is, for example, at least sectionally straight, and which extends from the first connecting strut to the third connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, exclusively on a side of said longitudinal section plane occupied both by the first as well as also by the third measuring tube, and a second longitudinal strut, which is, for example, at least sectionally straight, and which extends from the second connecting strut to the fourth connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, for example by the same distance as the first longitudinal strut, exclusively on a side of said longitudinal section plane occupied both by the second as well as also by the fourth measuring tube, and that the deformation body has a first cross brace, which, for example, extends from the first longitudinal strut to the second longitudinal strut, and which, for example, is at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane. The first cross brace can, for example, extend from the first connecting strut to the second connecting strut; and/or both the first connecting strut as well as also the second connecting strut can in each case be affixed with their respective first strut ends to the first cross brace; and/or the first cross brace, in a region in which it imaginarily intersects the second imaginary longitudinal section plane, can have a smaller cross section than it has in an adjoining, neighboring region extending to the first connecting strut, and a smaller cross section than it has in an adjoining, neighboring region extending to the second connecting strut.

Developing this embodiment further, it is additionally provided that the first cross brace has a minimal bending stiffness determined by a modulus of elasticity dependent on a material of said cross brace, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to said longitudinal strut, and that the first cross brace is arranged in such a manner, that the imaginary bending principal axis of its minimal areal moment of inertia extends parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane, and also does so, for example, in such a manner, that said imaginary bending principal axis lies in the second imaginary longitudinal section plane.

Alternatively or in supplementation of this, it is additionally provided that the deformation body has a second cross brace, which extends from the first longitudinal strut to the second longitudinal strut, and which, for example, is at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane, and/or is constructed equally to the first cross brace.

According to a tenth embodiment of the measuring transducer of the invention, it is additionally provided that the deformation body has at least two longitudinal struts—for example, equally constructed and/or plate-shaped longitudinal struts—of which a first longitudinal strut, which is, for example, at least sectionally straight, and which extends from the first connecting strut to the third connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, exclusively on a side of said longitudinal section plane occupied both by the first as well as also by the third measuring tube, and a second longitudinal strut, which is, for example, at least sectionally straight, and which extends from the second connecting strut to the fourth connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, for example by the same distance as the first longitudinal strut, exclusively on a side of said longitudinal section plane occupied both by the second as well as also by the fourth measuring tube, and that the deformation body has a first cross brace, which, for example, extends from the first longitudinal strut to the second longitudinal strut, and which, for example, is at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane, as well as a second cross brace, which extends from the first longitudinal strut to the second longitudinal strut, and which, for example, is at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane, and/or is constructed equally to the first cross brace. The first cross brace can, for example, extend from the first connecting strut to the second connecting strut; and/or both the first connecting strut as well as also the second connecting strut can in each case be affixed with their respective first strut ends to the first cross brace; and/or the first cross brace, in a region in which it imaginarily intersects the second imaginary longitudinal section plane, can have a smaller cross section than it has in an adjoining, neighboring region extending to the first connecting strut, and a smaller cross section than it has in an adjoining, neighboring region extending to the second connecting strut. Equally, the second cross brace can extend from the third connecting strut to the fourth connecting strut; and/or both the third connecting strut as well as also the fourth connecting strut can, in each case, be affixed with their respective first strut ends to the second cross brace; and/or the second cross brace, in a region in which this imaginarily intersects the second imaginary longitudinal section plane, can have a smaller cross section than it has in an adjoining, neighboring region extending to the third connecting strut, and a smaller cross section than it has in an adjoining, neighboring region extending to the fourth connecting strut. Furthermore, the two cross braces can each be formed by means of a flat rod. which, for example, is composed of metal, and/or they can each be composed of the same material and/or each be composed of steel.

Developing this embodiment further, it is additionally provided that the first cross brace has a minimal bending stiffness determined by a modulus of elasticity dependent on a material of said cross brace, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to said longitudinal strut, and that the first cross brace is arranged in such a manner, that the imaginary bending principal axis of its minimal areal moment of inertia extends parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane, and also does so, for example, in such a manner, that said imaginary bending principal axis lies in the second imaginary longitudinal section plane, and it is additionally provided that the second cross brace has a minimal bending stiffness determined by a modulus of elasticity dependent on a material of said cross brace, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to said longitudinal strut, and that the second cross brace is arranged in such a manner, that the imaginary bending principal axis of the minimal areal moment of inertia of the first cross brace extends parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane, and also does so, for example, in such a manner, that said imaginary bending principal axis of the minimal areal moment of inertia of the second cross brace lies in the second imaginary longitudinal section plane.

Alternatively or in supplementation, is additionally provided that the deformation body has a third longitudinal strut, which extends with a length from the first cross brace to the second cross brace, which is straight in projection on the imaginary cross sectional plane, and which, for example, is plate-shaped and/or parallel to the second imaginary longitudinal section plane and/or is in each case spaced an equal distance apart from the first longitudinal strut as from the second longitudinal strut.

According to an eleventh embodiment of the measuring transducer of the invention, it is additionally provided that the deformation body has longitudinal struts—for example, plate-shaped longitudinal struts—of which a first longitudinal strut, which is, for example, at least sectionally straight, and which extends from the first connecting strut to the third connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, exclusively on a side of said longitudinal section plane occupied both by the first as well as also by the third measuring tube, and a second longitudinal strut, which is, for example, at least sectionally straight, and which extends from the second connecting strut to the fourth connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, for example by the same distance as the first longitudinal strut, exclusively on a side of said longitudinal section plane occupied both by the second as well as also by the fourth measuring tube; that the deformation body has a first cross brace, which, for example, extends from the first longitudinal strut to the second longitudinal strut, and which, for example, is at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane, as well as a second cross brace, which extends from the first longitudinal strut to the second longitudinal strut, and which, for example, is at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane, and/or is constructed equally to the first cross brace; and that the deformation body has a third longitudinal strut, which extends with a length from the first cross brace to the second cross brace, which is straight in projection on the imaginary cross sectional plane, and which, for example, is plate-shaped and/or parallel to the second imaginary longitudinal section plane and/or is in each case spaced an equal distance apart from the first longitudinal strut as from the second longitudinal strut. Each of the longitudinal struts can in each case be formed, for example, by means of a flat rod, and/or in each case be composed of the same material, and/or in each case be composed of steel.

Developing this embodiment of the invention further, it is additionally provided that the third longitudinal strut is affixed with a first strut end to the first cross brace, especially in a region in which the first cross brace imaginarily intersects the second imaginary longitudinal section plane, and that the third longitudinal strut is affixed with a second strut end to the second cross brace, especially in a region, in which the second cross brace imaginarily intersects the second imaginary longitudinal section plane. Alternatively or in supplementation of this, it is additionally provided that the length of the third longitudinal strut is greater than 10% of the length f the first longitudinal strut and/or smaller than 120% of the length of the first longitudinal strut.

According to a twelfth embodiment of the measuring transducer of the invention, it is additionally provided that each of the connecting struts of the coupling element of the first type is at least sectionally straight, and especially predominantly or completely straight, in projection on the imaginary cross sectional plane.

According to a thirteenth embodiment of the measuring transducer of the invention, it is additionally provided that each of the connecting struts of the coupling element of the first type extends at least sectionally perpendicular to the first imaginary longitudinal section plane, and consequently parallel to the second imaginary longitudinal section plane. According to a fourteenth embodiment of the measuring transducer of the invention, it is additionally provided that each of the connecting struts of the coupling element of the first type has a straight subsection, which extends perpendicular to the first imaginary longitudinal section plane, and consequently parallel to the second imaginary longitudinal section plane. This occurs in such a manner, for example, that each of the connecting struts of the coupling element of the first type imaginarily intersects the first imaginary longitudinal section plane, for example, with its respective straight subsection, and, for example, at an angle of 90°.

According to a fifteenth embodiment of the measuring transducer of the invention, it is additionally provided that the first and the third connecting struts are oriented aligned relative to one another, and the second and fourth connecting struts are oriented aligned relative to one another.

According to a sixteenth embodiment of the measuring transducer of the invention, it is additionally provided that the first connecting strut has a maximum bending stiffness determined by a modulus of elasticity dependent on a material of the connecting strut, as well as also by a maximal areal moment of inertia about an imaginary bending principal axis immanent to said connecting strut, the second connecting strut has a maximum bending stiffness determined by a modulus of elasticity dependent on a material of the connecting strut, as well as also by a maximum areal moment of inertia about an imaginary bending principal axis immanent to the connecting strut, the third connecting strut has a maximum bending stiffness determined by a modulus of elasticity dependent on a material of the connecting strut, as well as also by a maximal areal moment of inertia about an imaginary bending principal axis immanent to the connecting strut, and the fourth connecting strut has a maximum bending stiffness determined by a modulus of elasticity dependent on a material of the connecting strut, as well as also by a maximum areal moment of inertia about an imaginary bending principal axis immanent to the connecting strut, and that each of the four connecting struts is in each case arranged in such a manner, that the imaginary bending principal axis of its maximal areal moment of inertia extends parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane. Developing this embodiment of the invention further, it is additionally provided that the maximum areal moment of inertia of the second connecting strut, as well as also the maximum areal moment of inertia of the third connecting strut and the maximum areal moment of inertia of the fourth connecting strut are in each case equal to the maximal areal moment of inertia the first connecting strut. Alternatively, or in supplementation to this, it is additionally provided that the first connecting strut has a minimum bending stiffness determined by a modulus of elasticity dependent on a material of the connecting strut, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to the connecting strut, the second connecting strut has a minimum bending stiffness determined by a modulus of elasticity dependent on a material of the connecting strut, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to the connecting strut, the third connecting strut has a minimum bending stiffness determined by a modulus of elasticity dependent on a material of the connecting strut, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to the connecting strut, and the fourth connecting strut has a minimum bending stiffness determined by a modulus of elasticity dependent on a material of the connecting strut, as well as also by a minimum areal moment of inertia about an imaginary bending principal axis immanent to the connecting strut, and that each of the four connecting struts is in each case arranged in such a manner, that the imaginary bending principal axis of its minimum areal moment of inertia extends parallel to the first longitudinal section plane and is perpendicular to the second imaginary longitudinal section plane.

According to a seventeenth embodiment of the measuring transducer of the invention, it is additionally provided that each of the connecting struts—which are, for example, equally constructed—are formed by means of a flat rod, which is, for example, at least sectionally curved in an S-shaped, Z-shaped, V-shaped and/or U-shaped manner in projection on the second imaginary longitudinal section plane; and/or that the first connecting strut, the second connecting strut, the third longitudinal strut and the fourth connecting strut are each composed of the same material and/or in each case composed of steel.

According to an eighteenth embodiment of the measuring transducer of the invention, it is additionally provided that the second measuring tube, the third measuring tube and fourth measuring tube each have an empty mass, which is equal to an empty mass of the first measuring tube; and/or that the first measuring tube has an empty mass, which is greater than 20 kg, and, for example, is also greater than 30 kg and/or smaller than 50 kg. Developing this embodiment of the invention further, it is additionally provided that the deformation body of the coupling element of the first type has a mass, which amounts to less than 50% of the empty mass of the first measuring tube, and, for example, is also greater than 10% of the empty mass, M₁₈, of the first measuring tube.

According to a nineteenth embodiment of the measuring transducer of the invention, it is additionally provided that each of the four measuring tubes in each case has a tube cross section determined by a caliber of said measuring tube as well as by a wall thickness of said measuring tube, wherein both the second measuring tube as well as also the third measuring tube and the fourth measuring tube each have a caliber, which in each case is equal to a caliber of the first measuring tube, and each also have a wall thickness, which is equal to a wall thickness, h₁₈, of the first measuring tube, and consequently both the second measuring tube as well as also the third measuring tube and the fourth measuring tube in each case have an outer diameter, which is equal to an outer diameter of the first measuring tube.

According to a twentieth embodiment of the measuring transducer of the invention, it is additionally provided that each of the four connecting struts, in each case, has a strut length defined by a minimum distance between their respective first strut ends and their respective second strut ends, and that both the second connecting strut as well as also the third as well as the fourth connecting strut in each case have a strut length, which, in each case, is equal to the strut length of the first connecting strut.

According to a twenty-first embodiment of the measuring transducer of the invention, the exciter mechanism is embodied in such a manner, that therewith, each of the four measuring tubes is excitable, for example, also simultaneously, to bending oscillations.

According to a twenty-second embodiment of the measuring transducer of the invention, the exciter mechanism is embodied in such a manner, that the first measuring tube and the second measuring tube are excitable to bending oscillations, which are opposite-equal relative to the second imaginary longitudinal section plane, and thus, for example, symmetrical relative to the second imaginary longitudinal section plane, and the third measuring tube and the fourth measuring tube are excitable to bending oscillations, which are opposite-equal relative to the second imaginary longitudinal section plane, and thus, for example, symmetrical relative to the second imaginary longitudinal section plane.

According to a twenty-third embodiment of the measuring transducer of the invention, the exciter mechanism is embodied in such a manner, that the first measuring tube and the third measuring tube are excitable to bending oscillations, which are opposite-equal relative to the second imaginary longitudinal section plane, and thus, for example, symmetrical relative to the second imaginary longitudinal section plane, and the second measuring tube and the fourth measuring tube are excitable to bending oscillations, which are opposite-equal relative to the second imaginary longitudinal section plane, and thus, for example, symmetrical relative to the second imaginary longitudinal section plane.

According to a twenty-fourth embodiment of the measuring transducer of the invention, the exciter mechanism is embodied in such a manner, that a natural bending oscillation mode of a first type inherent to the tube arrangement is excitable, wherein, in this bending oscillation mode of the first type, the first measuring tube and the second measuring tube execute bending oscillations—which are opposite-equal relative to the second imaginary longitudinal section plane, and thus, for example, symmetrical relative to the second imaginary longitudinal section plane—and in each case do so about a static rest position associated with the respective measuring tube—for instance, cantilever bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes—and wherein, in this bending oscillation mode of the first type, the third measuring tube and the fourth measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane, and thus, for example, symmetrical relative to the second imaginary longitudinal section plane, and in each case do so about a static rest position associated with the respective measuring tube—for instance, cantilever bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes—and do so in such a manner, that, relative to the second imaginary longitudinal section plane, the bending oscillations of the first measuring tube are thus opposite-equal to the bending oscillations of the third measuring tube, and that, relative to the second imaginary longitudinal section plane, the bending oscillations of the second measuring tube are thus opposite-equal to the bending oscillations of the fourth measuring tube.

Developing this embodiment of the invention further, the exciter mechanism is embodied in such a manner, that a natural bending oscillation mode of a second type inherent to the tube arrangement is excitable—also, for example, simultaneously with the bending oscillation mode of first type—wherein, in this bending oscillation mode of the second type, the first measuring tube and the second measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane, and thus, for example, symmetrical relative to the second imaginary longitudinal section plane, and in each case do so about a static rest position associated with the respective measuring tube—for instance cantilever, bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes—and wherein, in this bending oscillation mode of the second type, and wherein, in this bending oscillation mode of the first type, the third measuring tube and the fourth measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane, and thus, for example, symmetrical relative to the second imaginary longitudinal section plane, and in each case do so about a static rest position associated with the respective measuring tube—for instance, cantilever bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes—and do so in such a manner, that, relative to the second imaginary longitudinal section plane, said bending oscillations of the first measuring tube are thus opposite-equal to the bending oscillations of the third measuring tube, and that, relative to the second imaginary longitudinal section plane, the bending oscillations of the second measuring tube are thus opposite-equal to the bending oscillations of the fourth measuring tube.

Alternatively, or in supplementation, it is additionally provided that the eigenfrequency of the bending oscillation mode of the first type, for example, such an eigenfrequency as is measurable in the case of a tube arrangement completely filled with water, is different—for example, by more than 10 Hz—from an eigenfrequency of the bending oscillation mode of the second type, for example, such an eigenfrequency as is measurable in the case of a tube arrangement completely filled with water and/or measurable at the same time as the eigenfrequency of the bending oscillation mode of first type; e.g. in such a manner, that said eigenfrequency of the bending oscillation mode of the first type is greater more than 10 Hz than said eigenfrequency of the bending oscillation mode of the second type, or that said eigenfrequency of the bending oscillation mode of the first type is smaller by more than 10 Hz than said eigenfrequency of the bending oscillation mode of the second type.

According to a twenty-fifth embodiment of the invention, each of the four measuring tubes has a measuring tube peak, defined as the greatest perpendicular distance of the respective measuring tube from the first imaginary longitudinal section plane.

According to a twenty-sixth embodiment of the measuring transducer the invention, a center of mass of the tube arrangement lies in a imaginary cross sectional plane of the tube arrangement, which is in each case perpendicular both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane.

According to a twenty-seventh embodiment of the measuring transducer of the invention, the tube arrangement is mirror symmetrical relative to an imaginary cross sectional plane of the tube arrangement, which perpendicular both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane.

According to a twenty-eighth embodiment of the measuring transducer of the invention, each of the four measuring tubes has a measuring tube peak, defined as the greatest perpendicular distance of the respective measuring tube from the first imaginary longitudinal section plane, and an imaginary cross sectional plane of the tube arrangement perpendicular to both the first imaginary longitudinal section plane as well as also the second imaginary longitudinal section plane intersects each of the four measuring tubes at their respective measuring tube peaks.

According to a twenty-ninth embodiment of the measuring transducer of the invention, a middle segment of the transducer housing is at least partially formed by means of a straight—for example, circularly cylindrical—support tube, for instance, in such a manner, that a segment of the first measuring tube extending outwards from the support tube on a first side and a segment of the second measuring tube extending outwards from the support tube on the first side are surrounded by a first housing cap of the transducer housing, and that a segment of the third measuring tube extending outwards from the support tube on a second side lying opposite to the first side and a segment of the fourth measuring tube extending outwards from said support tube on the second side are surrounded by a second housing cap of the transducer housing, for example, a second housing cap constructed equally to the first housing cap.

According to a thirtieth embodiment of the measuring transducer of the invention, it is additionally provided that the two flow dividers are additionally embodied and arranged in the measuring transducer in such a manner, that an imaginary first connecting axis of the measuring transducer imaginarily connecting the first flow opening of the first flow divider with the first flow opening of the second flow divider extends parallel to an imaginary second connecting axis of the measuring transducer imaginarily connecting the second flow opening of the first flow divider with the second flow opening of the second flow divider, that an imaginary third connecting axis of the measuring transducer imaginarily connecting the third flow opening of the first flow divider with the third flow opening of the second flow divider extends parallel to an imaginary fourth connecting axis of the measuring transducer imaginarily connecting the fourth flow opening of the first flow divider with the fourth flow opening of the second flow divider. Developing this embodiment of the invention further, it is additionally provided that a first imaginary longitudinal section plane of the measuring transducer, within which the first imaginary connecting axis and the second imaginary connecting axis extend—for example, parallel to a principal flow axis of the measuring transducer aligning with the pipeline—is parallel to a second imaginary longitudinal section plane of the measuring transducer, within which the imaginary third connecting axis and the imaginary fourth connecting axis extend, for example, in such a manner, that the first imaginary longitudinal section plane of the tube arrangement lies between the first and second imaginary longitudinal section planes of the measuring transducer and/or is parallel to the first and second imaginary longitudinal section planes of the measuring transducer.

According to an thirty-first embodiment of the measuring transducer of the invention, it is additionally provided that the two flow dividers are embodied and arranged in the measuring transducer in such a manner, that a third imaginary longitudinal section plane of the measuring transducer, within which the imaginary first connecting axis and the imaginary third connecting axis extend, is parallel to a fourth imaginary longitudinal section plane of the measuring transducer, within which the imaginary second connecting axis and the imaginary fourth connecting axis extend. Developing this embodiment of the invention further, it is additionally provided that the second imaginary longitudinal section plane of the tube arrangement extends between the third imaginary longitudinal section plane of the measuring transducer and the fourth imaginary longitudinal section plane of the measuring transducer, for example, in such a manner, that the second imaginary longitudinal section plane of the tube arrangement is parallel to the third imaginary longitudinal section plane of the measuring transducer and parallel to the fourth imaginary longitudinal section plane of the measuring transducer.

According to a thirty-second embodiment of the measuring transducer of the invention, it is additionally provided that the four flow openings of the first flow divider are arranged in such a manner, that imaginary areal centers of gravity associated with cross sectional areas—especially circularly shaped cross sectional areas—of the flow openings of the first flow divider form the vertices of an imaginary rectangle or of an imaginary square, wherein said cross sectional areas lie in a shared imaginary cross sectional cutting plane of the first flow divider, for example, perpendicular to the first imaginary longitudinal section plane of the measuring transducer, or to the second imaginary longitudinal section plane of the measuring transducer.

According to a thirty-third embodiment of the measuring transducer of the invention, it is additionally provided that the four flow openings of the second flow divider are arranged in such a manner, that imaginary areal centers of gravity associated with cross sectional areas of the flow openings of the second flow divider form the vertices of an imaginary rectangle or of an imaginary square, wherein the cross sectional areas lie in a shared imaginary cross sectional cutting plane of the second flow divider, for example, perpendicular to the first imaginary longitudinal section plane of the measuring transducer, or to the second imaginary longitudinal section plane of the measuring transducer.

According to a thirty-fourth embodiment of the measuring transducer of the invention, it is additionally provided that each of the four measuring tubes, which are especially of an equal size, has a caliber, which amounts to more than 40 mm, especially more than 60 mm. Developing this embodiment of the invention further, it is additionally provided that the measuring tubes are bent and arranged in such a manner, that a caliber-to-height ratio of the tube arrangement, defined by a ratio of the caliber of the first measuring tube to a maximal lateral expanse of the tube arrangement measured from a peak of the first measuring tube to a peak of the third measuring tube, amounts to more than 0.05, especially more than 0.07 and/or less than 0.35, especially less than 0.2.

According to a thirty-fifth embodiment of the measuring transducer of the invention, it is additionally provided that the first flow divider has a flange, especially a flange having a mass of more than 50 kg, for connecting the measuring transducer to a tubular segment of the pipeline serving for supplying medium to the measuring transducer, and that the second flow divider has a flange, especially a flange having a mass of more than 50 kg, for connecting the measuring transducer to a segment of the pipeline serving for removing medium from the measuring transducer. Developing this embodiment of the invention further, each of the flanges has a sealing surface for fluid-tight connecting of the measuring transducer with the respective corresponding tubular segment of the pipeline, wherein a distance between the sealing surfaces of both flanges defines an installed length of the measuring transducer, especially an installed length amounting to more than 1000 mm and/or less than 3000 mm. The measuring transducer is additionally embodied in such a manner, that, in such case, a measuring tube length of the first measuring tube corresponding to a length of a section of the deflection curve of the first measuring tube extending between the first flow opening of the first flow divider and the first flow opening of the second flow divider is selected in such a manner, that a measuring-tube-length-to-installed-length ratio of the measuring transducer, as defined by a ratio of the measuring tube length of the first measuring tube to the installed length of the measuring transducer, amounts to more than 0.7, especially more than 0.8 and/or less than 1.2, and/or that a caliber-to-installed-length ratio of the measuring transducer, as defined by a ratio of a caliber of the first measuring tube to the installed length of the measuring transducer, amounts to more than 0.02, especially more than 0.05 and/or less than 0.09. Alternatively or in supplementation thereof, the measuring transducer is embodied in such a manner, that a-nominal-diameter-to-installed-length ratio of the measuring transducer, as defined by a ratio of the nominal diameter of the measuring transducer to the installed length of the measuring transducer, is smaller than 0.3, especially smaller than 0.2 and/or greater than 0.1, wherein the nominal diameter corresponds to a caliber of the pipeline, in whose course the measuring transducer is to be used.

In a thirty-sixth embodiment of the measuring transducer of the invention, it is additionally provided that a measuring tube length of the first measuring tube corresponding to a length of a section of the deflection curve of the first measuring tube extending between the first flow opening of the first flow divider and the first flow opening of the second flow divider amounts to more than 1000 mm, especially more than 1200 mm and/or less than 3000 mm, especially less than 2500.

In a thirty-seventh embodiment of the measuring transducer of the invention, it is additionally provided that each of the four measuring tubes, for example, four measuring tubes of equal caliber, are arranged in such a manner, that a smallest lateral separation of each of the four measuring tubes—for example, measuring tubes of equal length—from a housing side wall of the transducer housing is, in each case, greater than zero, for example, also greater than 3 mm and/or greater than twice a respective tube wall thickness; and/or that a smallest lateral separation between two neighboring measuring tubes in each case amounts to more than 3 mm and/or more than the sum of their respective tube wall thicknesses.

In a thirty-eighth embodiment of the measuring transducer of the invention, it is additionally provided that each of the flow openings is arranged in such a manner, that a smallest lateral separation of each of the flow openings from a housing side wall of the transducer housing in each case amounts to more than zero, for example also more than 3 mm, and/or more than twice a smallest tube wall thickness of the measuring tubes; and/or that a smallest lateral separation between the flow openings amounts to more than 3 mm and/or more than twice a smallest tube wall thickness of the measuring tubes.

According to a twenty-ninth embodiment of the measuring transducer of the invention, it is additionally provided that the exciter mechanism is embodied in such a manner, that the first measuring tube and the second measuring tube are excitable during operation to opposite-equal bending oscillations, and that the third measuring tube and the fourth measuring tube are excitable during operation to opposite-equal bending oscillations.

According to a fortieth embodiment of the measuring transducer of the invention, it is additionally provided that a mass ratio of an empty mass of the entire measuring transducer to an empty mass of the first measuring tube is greater than 10, especially greater than 15 and smaller than 25.

According to a forty-first embodiment of the measuring transducer of the invention, it is additionally provided that an empty mass, M₁₈, of the first measuring tube, especially of each of the measuring tubes, is greater than 20 kg, especially greater than 30 kg and/or smaller than 50 kg.

According to a forty-second embodiment of the measuring transducer of the invention, it is additionally provided that an empty mass of the measuring transducer is greater than 200 kg, especially greater than 300 kg.

According to a forty-third embodiment of the measuring transducer of the invention, it is additionally provided that a nominal diameter of the measuring transducer, which corresponds to a caliber of the pipeline in whose course the measuring transducer is to be used, amounts to more than 100 mm, especially more than 300 mm. Advantageously, the measuring transducer is additionally embodied in such a manner, that a mass-to-nominal-diameter ratio of the measuring transducer, as defined by a ratio of the empty mass of the measuring transducer to the nominal diameter of the measuring transducer, is smaller than 2 kg/mm, especially smaller than 1 kg/mm and/or greater than 0.5 kg/mm.

According to a forty-fourth embodiment of the measuring transducer of the invention, it is additionally provided that the first and the second measuring tubes are of equal construction, at least as regards a material of which their tube walls are in each case composed, and/or as regards their geometrical tube dimensions, especially a tube length, a tube wall thickness, a tube outer diameter and/or a caliber. According to a forty-fifth embodiment of the invention, it is additionally provided that the third and fourth measuring tubes are of equal construction, at least as regards a material of which their tube walls are in each case composed, and/or as regards their geometric tube dimensions, especially a tube length, a tube wall thickness, a tube outer diameter and/or a caliber.

According to a forty-sixth embodiment of the measuring transducer of the invention, it is additionally provided that all four measuring tubes are of equal construction as regards a material of which their tube walls are composed, and/or as regards their geometric tube dimensions, especially a tube length, a tube wall thickness, a tube outer diameter and/or a caliber.

According to a forty-seventh embodiment of the measuring transducer of the invention, it is additionally provided that a material of which the tube walls of the four measuring tubes are at least partially composed is titanium and/or zirconium and/or, for example, stainless and/or high strength steel, duplex steel and/or super duplex steel, or Hastelloy.

According to a forty-eighth embodiment of the measuring transducer of the invention, it is additionally provided that the transducer housing, the flow dividers and tube walls of the measuring tubes are in each case composed of steel, for example stainless steel.

According to a forty-ninth embodiment of the measuring transducer of the invention, it is additionally provided that the exciter mechanism is formed by means of a first oscillation exciter, especially an electrodynamic first oscillation exciter and/or a first oscillation exciter differentially exciting oscillations of the first measuring tube relative to the second measuring tube. The exciter mechanism is especially formed by means of a second oscillation exciter, for example, an electrodynamic second oscillation exciter and/or a second oscillation exciter differentially exciting oscillations of the third measuring tube relative to the fourth measuring tube. In such case, it is additionally provided that the first and second oscillation exciters are electrically interconnected in series, and in such a manner, that a combined driver signal excites combined oscillations of the first and third measuring tubes relative to the second and fourth measuring tube. The oscillation exciter of the exciter mechanism can be formed, for example, by means of a permanent magnet held on the first measuring tube and by means of a cylindrical coil permeated by the magnetic field of the permanent magnet and held on the second measuring tube, wherein the second oscillation exciter is formed by means of a permanent magnet held on the third measuring tube and a cylindrical coil permeated by the magnetic field of the permanent magnet and held on the fourth measuring tube.

According to a first further development of the invention, the measuring transducer further comprises a sensor arrangement reacting to vibrations of the measuring tubes, especially bending oscillations of the measuring tubes excited by means of the exciter mechanism, for example, an electro-dynamic sensor arrangement and/or one formed by means of oscillation sensors constructed equally to one another, wherein the sensor arrangement serves for producing oscillation signals representing vibrations—especially bending oscillations—of the measuring tubes.

According to a first embodiment of the first further development of the invention, it is provided that the sensor arrangement is formed by means of an inlet-side, first oscillation sensor—especially an electrodynamic inlet-side, first oscillation sensor and/or one which differentially registers oscillations of the first measuring tube relative to the second measuring tube—as well as by means of an outlet-side, second oscillation sensor—especially an electrodynamic outlet-side, second oscillation sensor and/or one which differentially registers oscillations of the first measuring tube relative to the second measuring tube—and especially in such a manner, that a measuring length of the measuring transducer corresponding to a length of a section of a deflection curve of the first measuring tube extending between the first oscillation sensor and the second oscillation sensor amounts to more than 500 mm, especially more than 600 mm and/or less than 1200 mm, and/or that a caliber-to-measuring-length ratio of the measuring transducer, defined by a ratio of a caliber of the first measuring tube to the measuring length of the measuring transducer amounts to more than 0.05, especially more than 0.09. Additionally, the first oscillation sensor can be formed by means of a permanent magnet held on the first measuring tube and a cylindrical coil held on the second measuring tube permeated by the permanent magnet's magnetic field, and the second oscillation sensor can be formed by means of a permanent magnet held on the first measuring tube and a cylindrical coil held on the second measuring tube permeated by the permanent magnet's magnetic field.

According to a second embodiment of the first further development of the invention, it is additionally provided that the sensor arrangement is formed by means of an inlet-side, first oscillation sensor—especially an electrodynamic inlet-side, first oscillation sensor and/or one which differentially registers oscillations of the first measuring tube relative to the second measuring tube; by means of an outlet-side, second oscillation sensor—especially an electrodynamic outlet-side, second oscillation sensor and/or one which differentially registers oscillations of the first measuring tube relative to the second measuring tube; by means of an inlet-side, third oscillation sensor—especially an electrodynamic inlet-side, third oscillation sensor and/or one which differentially registers oscillations of the third measuring tube relative to the fourth measuring tube; as well as by means of an outlet-side, fourth oscillation sensor—especially an electrodynamic outlet-side, fourth oscillation sensor and/or one which differentially registers oscillations of the third measuring tube relative to the fourth measuring tube, and especially in such a manner, that a measuring length of the measuring transducer corresponding to a length of a section of a deflection curve of the first measuring tube extending between the first oscillation sensor and the second oscillation sensor amounts to more than 500 mm, especially more than 600 mm and/or less than 1200 mm, and/or that a caliber-to-measuring-length ratio of the measuring transducer, defined by a ratio of a caliber of the first measuring tube to the measuring length of the measuring transducer amounts to more than 0.05, especially more than 0.09. In such case, the first and third oscillation sensors can advantageously be electrically interconnected in series in such a manner, that a common oscillatory signal represents shared inlet-side oscillations of the first and third measuring tube relative to the second and fourth measuring tube, and/or the second and fourth oscillation sensor can be electrically interconnected in series in such a manner, that a common oscillatory signal represents shared outlet-side oscillations of the first and third measuring tube relative to the second and fourth measuring tube. Alternatively or in supplementation, the first oscillation sensor can additionally can be formed by means of a permanent magnet held on the first measuring tube and a cylindrical coil held on the second measuring tube and permeated by the permanent magnet's magnetic field, and the second oscillation sensor can be formed by means of a permanent magnet held on the first measuring tube and cylindrical coil held on the second measuring tube and permeated by the permanent magnet's magnetic field; and/or the third oscillation sensor can be formed by means of a permanent magnet held on the third measuring tube and a cylindrical coil held on the fourth measuring tube and permeated by the permanent magnet's magnetic field, and the fourth oscillation sensor can be formed by means of a permanent magnet held on the third measuring tube and a cylindrical coil held on the fourth measuring tube and permeated by the permanent magnet's magnetic field.

According to a second further development of the measuring transducer of the invention, said measuring transducer further comprises: A first coupling element of a first type, which is spaced apart both from the first flow divider as well as also from the second flow divider, which is affixed on the inlet side to each of the four measuring tubes, and which serves for adjusting eigenfrequencies of natural oscillation modes of the tube arrangement (for example, bending oscillation modes); as well as a second coupling element of a first type, which is spaced apart both from the first flow divider as well as also from the second flow divider, which is affixed on the outlet side to each of the four measuring tubes, which is essentially constructed equally to the first coupling element of the first type, and which serves for adjusting eige{dot over (n)}frequencies of natural oscillation modes of the tube arrangement (for example, bending oscillation modes).

According to a first embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that each of the two coupling elements of the first type is symmetrical relative to the first imaginary longitudinal section plane of the tube arrangement.

According to a second embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that each of the two coupling elements of the first type is symmetrical relative to the second imaginary longitudinal section plane of the tube arrangement.

According to a third embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that both coupling elements of the first type are arranged symmetrically in the measuring transducer relative to an imaginary cross sectional plane of the tube arrangement perpendicular both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane of the tube arrangement.

According to a fourth embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that the two coupling elements of the first type are arranged equidistantly in the measuring transducer relative to an imaginary cross sectional plane of the tube arrangement perpendicular both to the first imaginary longitudinal section plane, as well as also to the second imaginary longitudinal section plane of the tube arrangement. According to a fifth embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that the two coupling elements of the first type are arranged extending parallel in the measuring transducer relative to an imaginary cross sectional plane of the tube arrangement perpendicular both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane of the tube arrangement.

According to a sixth embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that each of the two coupling elements of the first type is embodied and placed in the measuring transducer in such a manner, that they are symmetrical relative to the first imaginary longitudinal section plane of the tube arrangement and/or relative to the second imaginary longitudinal section plane of the tube arrangement.

According to a seventh embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that both the first coupling element of the first type as well as also the second coupling element of the first type are formed by means of plate-shaped elements.

According to an eight embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that each of the two coupling elements of the first type is at least sectionally bulged, for example in such a manner, that they are at least sectionally convex relative to an imaginary cross sectional plane of the tube arrangement extending between the first coupling element of the first type and the second coupling element of the first type, and perpendicular both to the first imaginary longitudinal section plane of the tube arrangement as well as also to the second imaginary longitudinal section plane of the tube arrangement.

According to a ninth embodiment of the second further development of the measuring transducer of the invention, it is additionally provided that both the first coupling element of the first type as well as also the second coupling element of the first type, as viewed from an imaginary cross sectional plane of the tube arrangement extending between the first coupling element of first type and the second coupling element of first type and perpendicular both to the first imaginary longitudinal section plane of the tube arrangement as well as also to the second imaginary longitudinal section plane of the tube arrangement, are at least sectionally convex relative to this cross sectional plane.

According to a third further development of the measuring transducer of the invention, the measuring transducer further comprises: 1) A first coupling element of a second type—for example, a plate shaped first coupling element of a second type—which, for the purpose of forming inlet-side oscillation nodes both for vibrations—for example bending oscillations—of the first measuring tube as well as also for vibrations—for example bending oscillations—of the second measuring tube opposite-equal thereto, is affixed on the inlet side to the first measuring tube and to the second measuring tube, for example, both to a tube segment of the first measuring tube extending between the first flow divider and the first coupling element of the first type, as well as also affixed to a tube segment of the second measuring tube extending between the first flow divider and the first coupling element of the first type; 2) a second coupling element of the second type, which is, for example, plate-shaped and/or constructed equally to the first coupling element of the second type and/or parallel to the first coupling element of the second type, and which, for the purpose of forming outlet-side oscillation nodes both for vibrations—for example bending oscillations—of the first measuring tube as well as also for vibrations—for example bending oscillations—of the second measuring tube opposite-equal thereto, is affixed on the outlet side to the first measuring tube and to the second measuring tube, for example, both to a tube segment of the first measuring tube extending between the second flow divider and the second coupling element of the first type as well as also to a tube segment of the second measuring tube extending between the second flow divider and the second coupling element of the first type; 3) a third coupling element of the second type, which is, for example, plate-shaped and/or constructed equally to the first coupling element of the second type and/or parallel to the second coupling element of the second type, and which, for forming inlet-side oscillation nodes both for vibrations—for example bending oscillations—of the third measuring tube as well as also vibrations—for example bending oscillations —of the fourth measuring tube opposite-equal thereto, is affixed on the inlet side, spaced apart both from the first flow divider as well as also from the second flow divider, to the third measuring tube and to the fourth measuring tube, for example, both to a tube segment of the third measuring tube extending between the first flow divider and the first coupling element of the first type as well as also to a tube segment of the fourth measuring tube extending between the first flow divider and the first coupling element of the first type; as well as 4) a fourth coupling element of the second type, which is, for example, plate shaped and/or constructed equally to the first coupling element of the second type and/or parallel to the first coupling element of the second type, and which, for the forming outlet-side oscillation nodes both for vibrations—for example bending oscillations—of the third measuring tube as well as also for vibrations—for example bending oscillations—of the fourth measuring tube opposite-equal thereto, is affixed on the outlet side, spaced apart both from the first flow divider as well as also from the second flow divider, as well as also from the first coupling element, to the third measuring tube and to the fourth measuring tube, for example, affixed both to a tube segment of the third measuring tube extending between the second flow divider and the second coupling element of the first type as well as also to a tube segment of the fourth measuring tube extending between the second flow divider and the second coupling element of the first type. According to this embodiment of the invention, the measuring transducer can be manufactured, for example, by first affixing both the first coupling element of the second type as well as also the second coupling element of the second type in each case to the first measuring tube and to the second measuring tube for producing a first measuring tube package, as well as by affixing both the third coupling element of the second type as well as also the fourth coupling element of the second type in each case to the third measuring tube and to the fourth measuring tube for producing a second measuring tube package; and thereafter affixing both the first coupling element of the first type as well as also the second coupling element of the first type in each case to at least one of—also, for example, to each of —the measuring tubes of the first measuring tube package and to at least one of—also for example, to each of—the measuring tubes of the second measuring tube package.

According to a first embodiment of the measuring system the invention, it is additionally provided that, during operation, the four measuring tubes simultaneously execute bending oscillations, excited by the exciter mechanism, for example, in a bending oscillation fundamental mode of first type. Developing this embodiment of the invention further, it is additionally provided that the exciter mechanism effects oscillations of the measuring tubes, especially bending oscillations in the first bending oscillation mode of first type, by providing that an exciter force generated by means of the first oscillation exciter and acting on the first measuring tube is opposite, for example, also opposite-equal, to an exciter force generated at the same time by means of the first oscillation exciter and acting on the second measuring tube.

According to a second embodiment of the measuring system of the invention, it is additionally provided that the exciter mechanism includes at least a first oscillation exciter—for example, a first oscillation exciter acting differentially on the first and second measuring tubes and, for example, affixed thereto, and/or an electro-dynamic, first oscillation exciter—for converting electrical excitation power into the exciter mechanism fed by means of the transmitter electronics into mechanical exciter forces, for example, exciter forces having at least one signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of the tube arrangement, these exciter forces effecting variable and/or periodic bending oscillations of the first measuring tube and bending oscillations of the second measuring tube opposite-equal to the bending oscillations of the first measuring tube relative to the second imaginary longitudinal section plane of the tube arrangement. Developing this embodiment of the invention further, it is additionally provided that the first oscillation exciter is formed by means of a permanent magnet held on the first measuring tube, for example, in the region of a measuring tube peak, and by means of a cylindrical coil permeated by the magnetic field of the permanent magnet and held on the second measuring tube, for example, in the region of a measuring tube peak. Alternatively or in supplementation, the exciter mechanism can also further comprise a second oscillation exciter, for example, one acting differentially on the third and fourth measuring tubes and, for example, affixed thereto, and/or an electro-dynamic exciter mechanism and/or one constructed equally to the first oscillation exciter and/or electrically serially connected with the first oscillation exciter, for converting electrical excitation power into the exciter mechanism fed by means of the transmitter electronics into mechanical exciter forces, for example, exciter forces having at least one signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of the tube arrangement, these exciter forces effecting variable and/or periodic bending oscillations of the third measuring tube and bending oscillations of the fourth measuring tube opposite-equal to the bending oscillations of the third measuring tube relative to the second imaginary longitudinal section plane of the tube arrangement. The second oscillation exciter can, in such case, be formed by means of a permanent magnet held on the third measuring tube, for example, in the region of a measuring tube peak, and by means of a cylindrical coil permeated by the magnetic field of the permanent magnet and held on the fourth measuring tube, for example, in the region of a measuring tube peak.

According to a third embodiment of the measuring system of the invention, it is additionally provided that the transmitter electronics feeds electrical excitation power into the exciter mechanism by means of at least one electrical driver signal supplied to the exciter mechanism, for example, a driver signal having a variable maximum voltage level and/or a variable maximum electrical current level, for example, a variable and/or at least at times periodic driver signal having at least one signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of the tube arrangement; and that the exciter mechanism converts the electrical excitation power, especially power dependent on a voltage level and on an electrical current level of the at least one driver signal, at least partially into both bending oscillations of the first measuring tube and bending oscillations of the second measuring tube opposite-equal to bending oscillations of the first measuring tube relative to the second imaginary longitudinal section plane of the tube arrangement, as well as also into bending oscillations of the third measuring tube and bending oscillations of the fourth measuring tube opposite-equal to bending oscillations of the third measuring tube relative to the second imaginary longitudinal section plane of the tube arrangement. Developing this embodiment of the invention further, it is additionally provided that the at least one driver signal is fed to the first oscillation exciter, for instance in such a manner, that a first exciter current driven by a variable first exciter voltage provided by means of the first driver signal flows through its cylindrical coil. Alternatively or in supplementation, the at least one driver signal can have a plurality of signal components with signal frequencies different from one another, wherein at least one of the signal components of the first driver signal, for instance, a signal component dominating as regards signal power, has a signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of the tube arrangement, for example, an eigenfrequency of the bending oscillation mode of first type, in which each of the four measuring tubes executes bending oscillations.

According to a fourth embodiment of the measuring system of the invention, it is additionally provided that the transmitter electronics, based on electrical excitation power converted in the exciter mechanism, generates a viscosity measured value representing viscosity of the flowing medium; and/or that the transmitter electronics, based on oscillation signals delivered by the measuring transducer, generates a mass flow measured value representing the mass flow rate of the flowing medium and/or a density measured value representing density of the flowing medium.

A basic idea of the invention is to provide by means of a deformation body coupled via connecting struts with each of the measuring tubes—for example, a deformation body embodied as a frame construction or interconnection of struts—a coupling element serving for adjusting eigenfrequencies of natural oscillation modes of a tube arrangement of the type being discussed for a measuring transducer of vibration type, wherein this coupling element has a spring stiffness effective for the V-mode, which is different from a spring stiffness effective for the X-mode to such a degree, that, as a result, a sufficiently high frequency separation between the eigenfrequencies of the V- and of the X-mode, and consequently a mutual separation of the V-mode and the X-mode is brought about. This occurs not least of all also in such a manner, that the V-mode ultimately serving as the wanted mode is itself influenced as little as possible, that is to say is changed as little as possible with respect to its original eigenfrequency, that is to say its eigenfrequency in the case of said tube arrangement without the coupling element. This is in the present case also achieved by the coupling element being formed in the form of an interconnection of a plurality of spring subelements—for instance, spring subelements embodied in the form of rod or plate springs—which act in the directions of the principal axes of the tube arrangement, namely in the direction of the transverse axis (X-direction), the vertical axis (Y-direction) or the longitudinal axis (X-direction), or about said principal axes with bending and/or tension stiffnesses which in part differ to a considerable degree.

An advantage of the invention lies, among other things, additionally in the fact that, via use of one or more coupling elements of the type being discussed, the possibilities for use of tube arrangements with four curved measuring tubes in measuring transducers of vibration type are drastically improved in a simple, as well as very effective manner. By application of curved measuring tubes, lasting mechanical stresses, for example, as a result of thermally related expansion of the measuring tubes or as a result of clamping forces introduced into the measuring transducer because of the tube arrangement, are in turn largely prevented within the tube arrangement, or at least kept very low, and, as a result, the accuracy of measurement, as well as also the structural integrity of the measuring transducer, are safely maintained, even in the case of extremely hot media, or in the case of temperature gradients strongly fluctuating within the tube arrangement as a function of time. Moreover, due to the symmetry characteristics of the tube arrangement, also those transverse forces caused by bending oscillations of curved measuring tubes can largely be neutralized, which—as is discussed, among other things, in the previously mentioned EP-A 1 248 084 and U.S. Pat. No. 7,350,421—act essentially perpendicularly to the longitudinal section planes of the measuring transducer or its tube arrangement, specifically in the Y-direction, and can be quite damaging for the accuracy of measurement of measuring transducers of vibration type. Additionally, in the case of measuring transducers of the aforementioned type, in comparison to conventional measuring transducers with only one or two bent measuring tubes, an increased oscillation quality factor of the measuring transducer as a whole could be detected, this being especially a result of a significantly lessened dissipation of oscillatory energy from the measuring transducer into the pipeline connected thereto, for instance, as a result of actually undesired deformation of the flow dividers. Moreover, oscillations, especially in the V-mode, of the measuring tubes of measuring transducers according to the present invention also are, in comparison to conventional measuring transducers, influenced to a significantly lesser degree by pressure jolts and sound.

A further advantage the invention is additionally to be seen in the fact that by application of coupling elements of the type being discussed, for example, coupling elements embodied as an interconnection of individual rod- or plate-shaped spring portions, recourse can also by all means be made to conventional tubular shapes, and, as a result of this, predominantly established structural designs, for instance as regards materials used, joining technology, manufacturing steps, etc., or these need only be slightly modified. As a result of this, the manufacturing costs as a whole can also be kept to a level, which is equal, for instance, to that of conventional measuring transducers of vibration type of an equal nominal diameter. In this regard, a further advantage of the invention is to be found in the fact that, as a result of this, not only is an opportunity created for implementing comparatively compact measuring transducers of vibration type even with large nominal diameters of over 150 mm (and especially with a nominal diameters of more than 250 mm) with manageable geometric dimensions and empty dimensions, but additionally, this can also be accomplished in an economically sensible manner.

The measuring transducer of the invention is consequently suitable not only for measuring mass flows in conventional measuring ranges of some few kilogram/hour up to some 100t/h, but also for measuring flowable media, which are conveyed in a pipeline with a caliber of greater 150 mm, especially of 300 mm or more. Additionally, the measuring transducer is also suitable for measuring mass flows, which are at least at times greater than 1000 t/h, especially at least at times amounting to more than 1500 t/h, such as can occur, for example, in the case of applications for measuring petroleum, natural gas or other petrochemical materials.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention, as well as other advantageous embodiments thereof, will now be explained in greater detail on the basis of examples of embodiments presented in the figures of the drawing. Equal parts are provided in the figures with equal reference characters; when required to avoid clutter or when it otherwise appears sensible, already mentioned reference characters are omitted in subsequent figures. Other advantageous embodiments or further developments, especially also combinations of aspects of the invention first explained only individually, will additionally become evident from the figures of the drawing, as well as also alone from the dependent claims. In particular, the figures of the drawing show as follows:

FIG. 1 and FIG. 2 an in-line measuring device, serving, for example, as a Coriolis flow/density/viscosity measuring device, in perspective and also partially sectioned side views;

FIGS. 3 a and 3 b a projection of the in-line measuring device of FIG. 1 in two different side views;

FIG. 4 a in perspective side view, a measuring transducer of vibration type having a tube arrangement formed by means of four bent measuring tubes as well as at least one coupling element serving for adjusting the eigenfrequencies of the tube arrangement, installed in an in-line measuring device of FIG. 1;

FIG. 4 b the tube arrangement of FIG. 4 a in perspective side view;

FIG. 4 c in an enlarged perspective side view, the coupling element of the tube arrangement according to FIG. 4 a or 4 b;

FIGS. 5 a and 5 b a projection of the measuring transducer of FIG. 4 a in two different side views;

FIGS. 6 a and 6 b projections of a tube arrangement of FIG. 4 b in two different side views; and

FIGS. 7 a and 7 b schematically, oscillation modes (V-mode; X-mode) of a tube arrangement of FIG. 4 a, 4 b, in each case in projection onto an imaginary cross sectional plane of said tube arrangement.

FIGS. 8 a and 8 b schematically, oscillation modes (V-mode; X-mode) of a coupling element according to FIG. 4 a, 4 b, serving for adjusting eigenfrequencies of the tube arrangement, in each case in projection on an imaginary cross sectional plane of said tube arrangement; and

FIG. 9 schematically, the coupling element according to FIG. 4 a, 4 b, or 8 a, 8 b, serving for adjusting eigenfrequencies of the tube arrangement, in projection on an imaginary longitudinal section plane of said tube arrangement.

DETAILED DESCRIPTION IN CONJUNCTION WITH THE DRAWINGS

FIGS. 1, 2 schematically show a measuring system 1, especially a measuring system embodied as a Coriolis mass flow and/or density measuring device, which especially serves for registering a mass flow m of a medium flowing in a pipeline (not shown for reasons of perspicuity) and for representing such in a mass flow measured value representing this mass flow instantaneously. The medium can be practically any flowable material, for example, a powder, a liquid, a gas, a vapor, or the like. Alternatively or in supplementation, measuring system 1 can, in given cases, also be used for measuring a density ρ and/or a viscosity η of the medium. The measuring system is especially provided for measuring media such as, for example, petroleum, natural gas or other petrochemical materials, which are flowing in a pipeline having a caliber greater than 250 mm, especially a caliber (=nominal diameter of the measuring system) of 300 mm or more. Not least of all, the measuring system is also provided for measuring flowing media of the aforementioned type, which are caused to flow with a mass flow rate of greater than 1000 t/h, especially greater than 1500 t/h; it can, however, also directly be dimensioned in such a manner, that it also is suitable for measuring in the case of smaller mass flow rates, for instance, also of less than 10 t/h, or for pipelines with a smaller caliber, for instance, also of less than 100 mm.

Measuring system 1, shown here in the form of an in-line measuring device, namely a measuring device, which can be inserted into the course of a pipeline, comprises, for such purpose: A measuring transducer 11 of vibration type, through which the medium being measured flows during operation; as well as, electrically connected with measuring transducer 11, a transmitter electronics 12 (which is here not shown in detail) for operating the measuring transducer and for evaluating oscillation signals delivered by the measuring transducer. In an advantageous manner, the transmitter electronics 12, which is formed, for example, by means of one or more microprocessors and/or by means of one or more digital signal processors, can, for example, be designed in such a manner, that during operation of the measuring system 1, it can exchange measuring and/or other operating data with a measured value processing unit superordinated to it, for example, a programmable logic controller (PLC), a personal computer and/or a work station, and do so via a data transmission system, for example, a hardwired fieldbus system and/or wirelessly per radio. Furthermore, the transmitter electronics 12 can be designed in such a manner, that it can be fed by an external energy supply, for example, also via the aforementioned fieldbus system. For the case, in which the measuring system 1 is provided for coupling to a fieldbus or other communication system, the transmitter electronics 12—for example, also a transmitter electronics, which is programmable on-site and/or via a communication system—can additionally include a corresponding communication interface for data communication, e.g. for sending the measured data to the already mentioned programmable logic controller or a superordinated process control system, and/or for receiving settings data for the measuring system.

FIGS. 4 a, 4 b, 5 a, 5 b, 6 a, 6 b show different representations of an example of an embodiment for a measuring transducer 11 of vibration type suited for the measuring system 1, especially one serving as a Coriolis mass flow, density and/or viscosity transducer, wherein measuring transducer 11 is applied during operation in the course of a pipeline (not shown), through which a medium to be measured, for example, a powdered, liquid, gaseous or vaporous medium, is flowing. As already mentioned, measuring transducer 11 serves to produce in a medium flowing therethrough such mechanical reaction forces —especially Coriolis forces dependent on the mass flow rate, inertial forces dependent on the density of the medium and/or frictional forces dependent on the viscosity of the medium —which react measurably, especially in a manner registerable via sensor, on the measuring transducer. Derived from these reaction forces describing the medium, by means of evaluating methods correspondingly implemented in the transmitter electronics in the manner known to those skilled in the art, the mass flow rate m (thus the mass flow), for example, and/or the density and/or the viscosity of the medium can be measured.

The measuring transducer 11 includes a transducer housing 7 ₁, which is here partially essentially tubular—and thus also externally partially circularly cylindrical—in which other components of the measuring transducer 11 serving for registering the at least one measured variable are accommodated so as to be protected against external environmental influences, thus dust or water spray or also any other kinds of forces acting externally on the measuring transducer. An inlet-side, first housing end of the transducer housing 7 ₁ is formed by means of an inlet-side, first flow divider 20 ₁, and an outlet-side, second housing end of the transducer housing 7 ₁ is formed by means of outlet-side, second flow divider 20 ₂. Each of the two flow dividers 20 ₁, 20 ₂, which are, in this respect, formed as integral components of the housing, includes four flow openings 20 _(1A), 20 _(1B), 20 _(1C), 20 _(1D), or 20 _(2A), 20 _(2B), 20 _(2C), 20 _(2D)—for example, circularly cylindrical or tapered or conical flow openings—each spaced from one another and/or each embodied as an inner cone. Moreover, each of the flow dividers 20 ₁, 20 ₂, which are, for example, manufactured from steel, is provided with a flange 6 ₁ or 6 ₂, which is, for example, manufactured of steel, and serves for connecting of the measuring transducer 11 to a tubular segment of the pipeline serving for supplying medium to the measuring transducer, or to a tubular segment of such pipeline serving for removing medium from the measuring transducer. According to an embodiment of the invention, each of the two flanges 6 ₁, 6 ₂ has a mass of more than 50 kg, especially more than 60 kg and/or less than 100 kg. For leakage-free and especially fluid-tight connecting of the measuring transducer with the respective corresponding tubular segment of the pipeline, each of the flanges additionally in each case includes a corresponding sealing surface 6 _(1A) or 6 _(2A), which is as planar as possible. A distance between the two sealing surfaces 6 _(1A), 6 _(2A) of both flanges thus for practical purposes defines an installed length, L₁₁, of the measuring transducer 11. The flanges are dimensioned, especially as regards their inner diameter, their respective sealing surface as well as the flange bores serving for accommodating corresponding connection bolts, according to the nominal diameter D₁₁ provided for the measuring transducer 11, as well as according to the industrial standards in given cases relevant therefor, which correspond to a caliber of the pipeline, in whose course the measuring transducer is to be used. As a result of the large nominal diameter especially desired for the measuring transducer, its installed length L₁₁ amounts, according to an embodiment of the invention, to more than 1200 mm. Additionally, it is, however, provided that the installed length of the measuring transducer 11 is kept as small as possible, especially smaller than 3000 mm. The flanges 6 ₁, 6 ₂ can, as is also directly evident from FIG. 4 a and is quite usual in the case of such measuring transducers, be arranged for this purpose as near as possible to the flow openings of the flow dividers 20 ₁, 20 ₂, in order to thus provide as short as possible an inlet (or outlet, as the case may be) region in the flow dividers, and thus to provide as a whole as short an installed length L₁₁ of the measuring transducer as possible, especially an installed length L₁₁ of less than 3000 mm. For a measuring transducer which is as compact as possible, and especially also in the case of high desired mass flow rates of over 1000 t/h, according to another embodiment of the invention, the installed length and the nominal diameter of the measuring transducer are dimensioned and matched to one another in such a manner, that a nominal-diameter-to-installed-length ratio D₁₁/L₁₁ of the measuring transducer, as defined by a ratio of the nominal diameter D₁₁ of the measuring transducer to the installed length L₁₁ of the measuring transducer, is smaller than 0.3, especially smaller than 0.2 and/or greater than 0.1. In the example of an embodiment shown here, at least one middle segment 7 _(1A) of the transducer housing 7 ₁ is formed by means of a straight tube—here also a circularly cylindrical and initially three-part tube—so that for manufacturing the transducer housing 7 ₁, welded or cast standard tubes, for example, also standardized and consequently cost effective welded or cast standard tubes, can be used, for example, tubes made of cast steel or forged steel. As is additionally directly evident from the combination of FIGS. 1 and 2, the middle segment 7 _(1A) of the transducer housing 7 ₁ can be formed, in such case, also for example by means of a tube having approximately the caliber of the pipeline it is to be connected to, and consequently corresponding to a nominal diameter D₁₁ of the measuring transducer, especially a tube corresponding as regards caliber, wall thickness and material to the pipeline it is to be connected to, and, in this respect, also correspondingly matched as regards the allowed operating pressure. Particularly for the case, in which the tubular middle segment as well as also the flow dividers connected with the respective flanges in the inlet and outlet regions in each case have the same inner diameter, the transducer housing can additionally also be formed in a manner such that the flanges are formed or welded on the ends of the tube forming the middle segment, and that the flow dividers are formed by means of plates having the flow openings, especially plates somewhat spaced apart from the flanges and welded orbitally to the inner wall and/or by means of laser welding.

For conveying the medium flowing at least at times through pipeline and measuring transducer, the measuring transducer of the invention additionally comprises a tube arrangement having four curved or bent, for example at least sectionally circular arc shaped, and/or—as shown here schematically—at least sectionally V-shaped measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, which are held oscillatably in the transducer housing 10. The four measuring tubes—in this case, measuring tubes of equal length and arranged pairwise in parallel—in each case communicate with the pipeline connected to the measuring transducer and are at least at times and especially also simultaneously caused during operation to vibrate in at least one actively excited oscillatory mode—the so-called wanted mode—suited for ascertaining the physical, measured variable. Of the four measuring tubes, a first measuring tube 18 ₁ opens with an inlet-side, first measuring tube end into a first flow opening 20 _(1A) of the first flow divider 20 ₁ and with an outlet-side, second measuring tube end into a first flow opening 20 ₂ of the second flow divider 20 ₂; a second measuring tube 18 ₂ opens with an inlet-side, first measuring tube end into a second flow opening 20 _(1B) of the first flow divider 20 ₁ and with an outlet-side, second measuring tube end into a second flow opening 20 _(2B) of the second flow divider 20 ₂; a third measuring tube 18 ₃ opens with an inlet-side, first measuring tube end into a third flow opening 20 _(1C) of the first flow divider 20 ₁ and with an outlet-side, second measuring tube end into a third flow opening 20 _(2C) of the second flow divider 20 ₂; and a fourth measuring tube 18 ₄ opens with an inlet-side, first measuring tube end into a fourth flow opening 20 ₁) of the first flow divider 20 ₁ and with an outlet-side, second measuring tube end into a fourth flow opening 20 _(2D) of the second flow divider 20 ₂. The four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are thus connected to the flow dividers 20 ₁, 20 ₂—which are especially equally constructed flow dividers 20 ₁, 20 ₂—to form flow paths connected in parallel, and indeed in a manner enabling vibrations, especially bending oscillations, of the measuring tubes relative to one another, as well as also relative to the transducer housing. Additionally, it is provided that the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are held oscillatably in the transducer housing 7 ₁—here, namely on its middle segment 7 _(1A)—only by means of said flow dividers 20 ₁, 20 ₂. Suitable as material for the tube walls of the measuring tubes is, for example, stainless steel (in given cases, also high strength stainless steel), titanium, zirconium or tantalum, or alloys formed therewith or also super alloys, such as, for instance, Hastelloy, Inconel etc. Moreover, the material for the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ can also be practically any other material usually used therefor, or at least a material suitable therefor, especially one with as small a thermal expansion coefficient as possible and as high a yield point as possible.

Alternatively or in supplementation, according to an additional embodiment of the invention, at least the first and second measuring tubes 18 ₁, 18 ₂ are of equal construction as regards the material of their tube walls and/or as regards their geometric tube dimensions, especially a measuring tube length, a tube outer diameter, a tube wall thickness and/or a caliber, and consequently as regards a tube cross section in each case determined by a caliber and wall thickness each of the measuring tube. Additionally, also at least the third and the fourth measuring tube 18 ₃, 18 ₄ are of equal construction as regards the material of their tube walls, and/or as regards their geometric tube dimensions, especially as regards a measuring tube length, a tube outer diameter, a tube wall thickness and/or a caliber, so that, as a result, the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are, at least pairwise, essentially of equal construction. Preferably, the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are of equal construction as regards the material of their tube walls, and/or as regards their geometric tube dimensions, especially a measuring tube length, a tube wall thickness, a tube outer diameter, a form of their bending lines and/or a caliber, especially in such a manner, that the four measuring tubes in each case have the same tube cross section, namely that both the second measuring tube as well as also the third measuring tube and the fourth measuring tube in each case have a caliber, which in each case is equal to a caliber, D₁₈, of the first measuring tube, as well as in each case have a wall thickness, which is equal to a wall thickness, h₁₈, of the first measuring tube, and consequently both the second measuring tube as well as also the third measuring tube and the fourth measuring tube in each case have an outer diameter, which is equal to an outer diameter, D₁₈+2·h₁₈, of the first measuring tube, so that also an areal moment of inertia of each of the measuring tubes dependent on caliber and wall thickness, and—in the case of use also of the same materials for all four measuring tubes —both the second measuring tube as well as also the third measuring tube and the fourth measuring tube in each case have a bending stiffness dependent on the modulus of elasticity determined by the material of the respective measuring tube as well as on the respective areal moment of inertia, this bending stiffness in each case being equal to the bending stiffness, E₁₈·J₁₈, of the first measuring tube, or have an empty mass, which is equal to an empty mass, M₁₈, of the first measuring tube. As a result of this, for this case, also at least one minimum bending oscillation resonance frequency of each of the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ (empty or uniformly flowed-through by a homogeneous medium) essentially equals the respective minimum bending oscillation resonance frequencies of the remaining other measuring tubes.

In the case of the measuring transducer of the invention, the measuring tubes are, as is also directly evident from the combination of FIGS. 2, 4 a and 4 b, additionally embodied and arranged in the measuring transducer in such a manner, that the tube arrangement has, lying both between the first measuring tube 18 ₁ and the third measuring tube 18 ₃ as well as also between the second measuring tube 18 ₂ and the fourth measuring tube 18 ₄, a first imaginary longitudinal-section plane XZ, with respect to which the tube arrangement is mirror symmetric, and in such a manner that the tube arrangement furthermore has, perpendicular to its imaginary first longitudinal-section plane XZ, and extending both between the first measuring tube 18 ₁ and second measuring tube 18 ₂ as well as also between the third measuring tube 18 ₃ and fourth measuring tube 18 ₄, a second imaginary longitudinal-section plane YZ, with respect to which the tube arrangement likewise is mirror symmetric. As a result of this, not only are stresses generated by possible thermally related expansion of the measuring tubes within the tube arrangement minimized, but also transverse forces possibly induced by the bending oscillations of the bent measuring tubes within the tube arrangement and acting essentially perpendicularly to the line of intersection of the two aforementioned imaginary longitudinal section planes can be largely neutralized, and not least of all also those transverse forces mentioned, among other things, also in the previously mentioned EP-A 1 248 084 and U.S. Pat. No. 7,350,421, are directed essentially perpendicular to the first imaginary longitudinal-section plane XZ. As is especially also evident from FIGS. 4 a, 4 b, 5 a, 5 b, in the example of an embodiment shown here, each of the four measuring tubes has a measuring tube peak, defined as the greatest perpendicular distance of the respective measuring tube from the first imaginary longitudinal section plane XZ. Apart from this, the tube arrangement has, as is also directly evident from the combination of FIGS. 4 a-6 b, an imaginary cross sectional plane XY perpendicular both to the first imaginary longitudinal section plane XZ as well as also to the second imaginary longitudinal section plane YZ. In an advantageous embodiment of the invention, the tube arrangement is additionally embodied in such a manner, that a center of mass of the tube arrangement lies in the imaginary cross sectional plane XY, or that the tube arrangement is mirror symmetric relative to the imaginary cross sectional plane XY, for instance, in such a manner, that the imaginary cross sectional plane XY intersects each of the four measuring tubes in its respective measuring tube peak.

For additional symmetrization of the measuring transducer and, thus, also for additional simplifying of its construction, the two flow dividers 20 ₁, 20 ₂ are, according to an additional embodiment of the invention, additionally embodied in such a manner and arranged in the measuring transducer in such a manner, that, as is also schematically presented in FIGS. 4 a and 4 b, an imaginary first connecting axis Z₁ of the measuring transducer imaginarily connecting the first flow opening 20 _(1A) of the first flow divider 20 ₁ with the first flow opening 20 _(2A) of the second flow divider 20 ₂ extends parallel to an imaginary second connecting axis Z₂ of the measuring transducer imaginarily connecting the second flow opening 20 _(1B) of the first flow divider 20 ₁ with the second flow opening 20 _(2B) of the second flow divider 20 ₂, and that an imaginary third connecting axis Z₃ of the measuring transducer imaginarily connecting the third flow opening 20 _(1C) of the first flow divider 20 ₁ with the third flow opening 20 _(2C) of the second flow divider 20 ₂ extends parallel to an imaginary fourth connecting axis Z₄ of the measuring transducer imaginarily connecting the fourth flow opening 20 _(1D) of the first flow divider 20 ₁ with the fourth flow opening 20 _(2B) of the second flow divider 20 ₂. As shown in FIGS. 4 a and 4 b, the flow dividers are additionally embodied in such a manner and arranged in the measuring transducer in such a manner, that the connecting axes Z₁, Z₂, Z₃, Z₄ also are parallel to a principal flow axis L of the measuring transducer essentially aligning with the pipeline and/or coincident with the aforementioned line of intersection of the two imaginary longitudinal section planes XZ, YZ of the tube arrangement. Furthermore, the two flow dividers 20 ₁, 20 ₂ can additionally also be embodied in such a manner and arranged in the measuring transducer in such a manner, that a first imaginary longitudinal-section plane XZ₁ of the measuring transducer, within which the first imaginary connecting axis Z₁ and the second imaginary connecting axis Z₂ extend, is parallel to a second imaginary longitudinal section plane XZ₂ of the measuring transducer, within which the imaginary third connecting axis Z₃ and the imaginary fourth connecting axis Z₄ extend. Additionally, the measuring tubes are advantageously arranged in such a manner, that the tube arrangement has a minimum distance between the second measuring tube and the fourth measuring tube, ultimately also determined by a minimum distance between the second and fourth flow opening of the first flow dividers, or the second and fourth flow opening of the second flow divider, wherein this minimum distance is equal to a minimum distance, A₁₈, between the first measuring tube and the third measuring tube, ultimately determined by a minimum distance between the first and third flow openings of the first flow divider, or the first and third flow openings of the second flow divider.

Moreover, the measuring tubes are, according to an additional embodiment of the invention, additionally embodied in such a manner and arranged in the measuring transducer in such a manner, that the imaginary first longitudinal section plane XZ of the tube arrangement—as is, among other things, also evident from the combination of FIGS. 3 a and 4 a—lies between the aforementioned first imaginary longitudinal section plane XZ₁ of the measuring transducer and the aforementioned second imaginary longitudinal section plane XZ₂ of the measuring transducer, for example, also such that the first longitudinal section plane XZ of the tube arrangement is parallel to the first and second longitudinal section planes XZ₁,XZ₂ of the measuring transducer. Additionally, the measuring tubes are embodied and arranged in the measuring transducer in such a manner, that likewise, also the second imaginary longitudinal section plane YZ of the tube arrangement extends between the third imaginary longitudinal section plane YZ₁ of the measuring transducer and the fourth imaginary longitudinal section plane YZ₂ of the measuring transducer, for instance in such a manner, that the second imaginary longitudinal section plane YZ of the tube arrangement is parallel to the third imaginary longitudinal section plane YZ₁ of the measuring transducer and parallel to the fourth imaginary longitudinal section plane YZ₂ of the measuring transducer. In the example of an embodiment shown here, the tube arrangement is, as is directly evident from the combination of FIGS. 4 a, 4 b, 5 a, 5 b and 6 a, additionally embodied in such a manner and placed in the transducer housing in such a manner, that, as a result, not only the shared line of intersection of the first and second imaginary longitudinal section planes XZ, YZ of the tube arrangement is parallel or coincident with the longitudinal axis L, but also a shared line of intersection of the first longitudinal section plane XZ and the cross sectional plane XY is parallel to an imaginary transverse axis Q of the measuring transducer perpendicular to the longitudinal axis L, and a shared line of intersection of the second longitudinal section plane YZ and the cross sectional plane XY is parallel to an imaginary vertical axis V of the measuring transducer perpendicular to the longitudinal axis L.

In an additional advantageous embodiment of the invention, the flow openings of the first flow divider 20 ₁ are additionally arranged in such a manner, that those imaginary areal centers of gravity, which belong to the—here circularly shaped —cross sectional areas of the flow openings of the first flow divider form the vertices of an imaginary rectangle or of an imaginary square, wherein said cross sectional areas lie, in turn, in a shared imaginary, cross sectional plane of the first flow divider extending perpendicular to a longitudinal axis L of the measuring transducer—for example, a longitudinal axis extending within the first longitudinal section plane XZ, of the tube arrangement, or parallel to or even coincident with the mentioned principal flow axis of the measuring transducer—or perpendicular to the longitudinal section planes of the measuring transducer. Additionally, the flow openings of the second flow divider 20 ₂ also are arranged in such a manner, that imaginary areal centers of gravity associated with—here likewise circularly shaped—cross sectional areas of the flow openings of the second flow divider 20 ₂ form the vertices of an imaginary rectangle or square, wherein said cross sectional areas lie, in turn, in a shared imaginary, cross sectional plane of the second flow divider extending perpendicular to the mentioned main flow axis or also longitudinal axis L of the measuring transducer, or perpendicular to the longitudinal section planes of the measuring transducer. In an additional embodiment of the invention, the measuring tubes are bent in such a manner and arranged in the measuring transducer in such a manner, that a caliber-to-height ratio D₁₈/Q₁₈ of the tube arrangement, defined by a ratio of the caliber, D₁₈, of the first measuring tube to a maximal lateral expanse of the tube arrangement Q₁₈, measured from a peak of the first measuring tube to a peak of the third measuring tube, or measured from a peak of the second measuring tube to a peak of the fourth measuring tube, amounts to more than 0.05, especially more than 0.07 and/or less than 0.35, especially less than 0.2.

For the purpose of implementing as compact a measuring transducer as possible, especially also for the mentioned case, in which such should have a comparatively large nominal diameter of 250 mm or more, and/or that the measuring tubes are comparatively spread out in a lateral direction, the transducer housing 7 ₁ can advantageously—as is additionally directly evident from the combination of FIGS. 1 and 2—additionally be formed by providing that the transducer housing 7 ₁ is formed by means of a tube and housing caps. The tube is here, for the purpose of simplified treatment, for example, initially three-part, thus three individual segments joined together, and has corresponding lateral openings for the caps. The tube has, for instance—as already indicated —the caliber of the pipeline it is to be connected to, thus a caliber corresponding to a nominal diameter D₁₁ of the measuring transducer. The housing caps 7 ₁₈, 7 _(1C), especially equally-constructed housing caps, are affixed laterally, for instance via welding, to the tube ultimately forming the middle segment of the transducer housing, and extend laterally from the middle segment to encase the segments of the measuring tubes. Of the two housing caps 7 _(1B), 7 _(1C)—as is evident from the combination of FIGS. 1-4 a—a first housing cap 7 _(1B), for example, caps a segment of the first measuring tube extending outwards on a first side from the middle segment—especially a middle segment serving also as a support frame for the tube arrangement, and consequently formed as a support tube—and a segment of the second measuring tube extending outwards on the first side from the middle segment, and a second housing cap 7 _(1C), for instance, a second housing cap constructed equally to the first housing cap, caps a segment of the third measuring tube extending outwards from the middle segment on a second side lying opposite the first side, and a segment of the fourth measuring tube extending outwards from the middle segment on the second side. As a result of this, the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, or the tube arrangement of the measuring transducer 11 formed therewith, are, as is directly evident from the combination of FIGS. 1, 2 and 4 a, completely encased by the transducer housing 7 ₁—formed here by means of the middle segment serving especially also as a support tube, as well as by the two housing caps laterally affixed thereto. For the aforementioned case, in which the transducer housing is formed by means of the tubular middle segment and the housing caps laterally affixed thereto, the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ and the transducer housing 7 ₁ are, in an additional embodiment of the invention—especially also for the purpose of minimizing the installed mass of the total measuring transducer—matched to one another, and furthermore dimensioned in such a manner, that a support-tube-to-measuring-tube-inner-diameter ratio of the measuring transducer, defined by a ratio of the largest inner diameter of the middle segment of the transducer housing formed as a support tube to a caliber D₁₈ of the first measuring tube, is greater than 3 and/or smaller than 5, especially smaller than 4.

Moreover, as material for the transducer housing 7 ₁, steels can be used, such as, for instance, structural steel or stainless steel, or also other high-strength materials suitable or usually suitable for such purpose. For most applications of industrial measurements technology, especially also in the petrochemical industry, measuring tubes of stainless steel, for example, also duplex steel, super duplex steel or another (high-strength) stainless steel, can additionally also satisfy the requirements regarding mechanical strength, chemical resistance as well as thermal requirements, so that in numerous cases of application, the transducer housing 7 ₁, the flow dividers 20 ₁, 20 ₂, as well as also the tube walls of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ can in each case be made of steel of in each case of sufficiently high quality, which, especially with respect to the material costs and manufacturing costs, as well as also to the thermally related dilation behavior of the measuring transducer 11 during operation, can be advantageous. Moreover, the transducer housing 7 ₁ can advantageously additionally also be embodied in such a manner and dimensioned in such a manner, that, in the case of possible damages to one or a number of the measuring tubes, e.g. through crack formation or bursting, outflowing medium can be completely retained in the interior of the transducer housing 7 ₁ up to a required maximal positive pressure and for as long as desired, wherein such a critical state can—as, for example, is also mentioned in the previously cited U.S. Pat. No. 7,392,709—be registered and signaled as early as possible by means of corresponding pressure sensors and/or based on operating parameters internally produced during operation by the mentioned transmitter electronics 12. For simplifying transport of the measuring transducer or of the entire in-line measuring device formed therewith—as is, for example, also provided in the previously mentioned U.S. Pat. No. 7,350,421—transport eyes can be provided on the inlet side and outlet sides, affixed externally on the transducer housing.

As already previously mentioned, the reaction forces required for the measuring are effected in the measuring transducer 11 in the medium to be measured by causing the measuring tubes 18 _(k), 18 ₂, 18 ₃, 18 ₄ to oscillate, for example, simultaneously, in an actively excited oscillatory mode: The so-called wanted mode. For exciting oscillations of the measuring tubes, especially also those in the wanted mode, the measuring transducer further comprises an exciter mechanism 5 formed by means of at least one electro-mechanical—for example, electro-dynamic—oscillation exciter acting on the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄. Exciter mechanism 5 serves to cause each of the measuring tubes operationally at least at times to execute oscillations, especially bending oscillations, in the wanted mode, and to maintain these wanted oscillations oscillations with oscillation amplitudes sufficiently large for producing in the medium—and for registering—the above named reaction forces suitable for the particular measuring. The at least one oscillation exciter, and thus the exciter mechanism formed therewith, serves, in such case, especially for converting an electrical excitation power P_(exc) fed from the transmitter electronics—for instance, by means of at least one electrical driver signal—into such exciter forces F_(exc), e.g. pulsating or harmonic exciter forces F_(exc), which act as simultaneously as possible, and uniformly, but in opposite directions, on at least two of the measuring tubes (for instance, the first and second measuring tubes) and, in given cases, are also coupled mechanically from the two measuring tubes further onto the other two measuring tubes, and thus effect oscillations in the wanted mode. The exciter forces F_(exc) generated by converting electrical excitation power P_(exc) fed into the exciter mechanism can, in the manner known to those skilled in the art, e.g. by means of an operating circuit provided in the transmitter electronics 12 and ultimately delivering the driver signal, be adjusted as regards their amplitude, for instance, by means of electrical current and/or voltage controllers implemented in the operating circuit; and can be adjusted as regards their frequency, for example, by means of an in operating circuit likewise provided phase control loop (PLL); also compare to this, for example, U.S. Pat. No. 4,801,897 or U.S. Pat. No. 6,311,136. In an additional embodiment of the invention, it is, consequently, additionally provided that, for generating the exciter forces, the transmitter electronics feeds required electrical excitation power into the exciter mechanism by means of at least one electrical driver signal—for example, an at least at times periodic driver signal—supplied to the oscillation exciter, and thus to the exciter mechanism, for example, via connecting lines. The driver signal is variable, with at least one signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of the tube arrangement, for instance, one in which each of the four measuring tubes, as is quite usual in the case of measuring transducers of vibration type with curved measuring tubes, executes bending oscillations about a particular static rest position, in the manner of a cantilever clamped at one end. For example, the at least one driver signal can also have a plurality of signal components with signal frequencies differing from one another, of which at least one signal component (for instance, one dominating as regards signal power) has a signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of the tube arrangement, in which each of the four measuring tubes executes bending oscillations, thus, for example, the mentioned bending oscillation mode of the first type. Moreover, it can additionally be advantageous—for instance, for the purpose of matching the fed-in excitation power to that amount instantaneously actually necessary for a sufficient oscillation amplitude—to make the at least one driver signal variable relative to a maximal voltage level (voltage amplitude) and/or a maximal electrical current level (electrical current amplitude)—for instance, in such a manner, that, for example, exciter current flows through the cylindrical coil of the at least one oscillation exciter driven by a variable exciter voltage provided by means of said driver signal.

An aim of the active excitation of the measuring tubes to oscillations is, in particular—especially also for the case, in which the measuring system ultimately formed by means of the measuring transducer should be used for measuring mass flow—to induce by means of the measuring tubes vibrating in the wanted mode sufficiently strong Coriolis forces in the flowing medium such that, as a result, additional deformations, and consequently deformations corresponding to an oscillatory mode of the tube arrangement of a higher order—the so-called Coriolis mode—of each of the measuring tubes can be effected with oscillation amplitudes sufficient for the measuring. For example, the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ can, by means of the electro-mechanical exciter mechanism held thereon, be excited to bending oscillations—especially simultaneous bending oscillations—especially at an instantaneous mechanical eigenfrequency of the tube arrangement formed by means of the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, in the case of which the measuring tubes are —at least predominantly—laterally deflected, and, as directly evident to those skilled in the art from the combination of FIGS. 3 a, 3 b, 6 a, 6 b, 7 a, 7 b, caused to oscillate pairwise essentially opposite-equally relative to one another. This occurs especially in such a manner, that, during operation, each of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ in each case at the same time executes vibrations at least at times and/or at least partially formed as bending oscillations about an imaginary oscillatory axis connecting the first and the particular associated second measuring tube end of the respective measuring tube, this oscillatory axis being parallel to each of the mentioned connecting axes Z₁, Z₂, Z₃, Z₄, wherein the four oscillatory axes are, in the example of an embodiment shown here, parallel to one another, as well as also to the imaginary longitudinal axis L of the entire measuring transducer, this longitudinal axis L imaginarily connecting the two flow dividers and passing through a center of mass of the measuring transducer. In other words, the measuring tubes can, as is quite usual in the case of measuring transducers of vibration type having one or more bent measuring tubes, be in each case caused to oscillate at least sectionally in the manner of a cantilever clamped at its ends—and consequently thus with cantilever-type, bending oscillations—in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes Z₁, Z₂, Z₃, Z₄. In an embodiment of the invention, the exciter mechanism is additionally embodied in, such a manner that, therewith, the first measuring tube 18 ₁ and the second measuring tube 18 ₂ are excitable to execute bending oscillations, which are opposite-equal relative to the second imaginary longitudinal section plane YZ, and especially also symmetric relative to the second imaginary longitudinal section plane YZ, and the third measuring tube 18 ₃ and the fourth measuring tube 18 ₄ are excitable to execute bending oscillations, which are opposite-equal relative to the second imaginary longitudinal section plane YZ, and especially also symmetric relative to the second imaginary longitudinal section plane YZ. As an alternative thereto or in supplementation thereof, the exciter mechanism is, according to an additional embodiment of the invention, additionally embodied in such a manner, that therewith, the first measuring tube 18 ₁ and the third measuring tube 18 ₃ are excitable to execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane YZ, and, for example, also symmetric relative to the second imaginary longitudinal section plane YZ, and the second measuring tube 18 ₂ and the fourth measuring tube 18 ₄ are excitable to execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane YZ, and, for example, symmetric relative to the second imaginary longitudinal section plane YZ.

In an additional embodiment of the invention, the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are additionally excited during operation by means of the exciter mechanism 5 at least partially, and especially predominantly, to wanted mode bending oscillations, which have a bending oscillation frequency, which, for instance, equals an instantaneous mechanical resonance frequency of the tube arrangement comprising the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, and consequently corresponds to an instantaneous eigenfrequency of a bending oscillation mode of the tube arrangement, or which lies at least in the vicinity of such an eigenfrequency or resonance frequency. The instantaneous mechanical resonance frequencies of bending oscillations are, in such case, as is known, dependent to an especial degree on the size, shape and material of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, as well as also on an instantaneous density of the medium flowing through the measuring tubes, and can thus vary during operation of the measuring transducer within a wanted frequency band of a width of quite some number of kilohertz. Thus, in the case of exciting the measuring tubes at an instantaneous resonance frequency, based on the instantaneously excited oscillation frequency, an average density of the medium flowing through the four measuring tubes can, on the one hand, instantaneously be easily ascertained. On the other hand, the electrical power instantaneously required for maintaining the oscillations excited in the wanted mode can thus also be minimized. The four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, driven by the exciter mechanism, are especially additionally caused to oscillate at least at times with essentially equal oscillation frequency, especially in each case with one and the same natural mechanical eigenfrequency, and thus with a shared, natural mechanical eigenfrequency. In an advantageous manner, the oscillatory behavior of the tube arrangement formed by means of the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, as well as also the driver signals controlling the exciter mechanism, are additionally matched to one another in such a manner, that at least the oscillations of the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ excited in the wanted mode are developed in such a manner, that the first and second measuring tubes 18 ₁, 18 ₂ oscillate—for instance, in the manner of two tuning fork tines—essentially opposite-equally to one another, and consequently at least in the imaginary cross sectional plane XY with an opposing phase shift of, for instance, 180°, and the third and the fourth measuring tube 18 ₃, 18 ₄ likewise also oscillate essentially opposite-equally to one another.

Investigations on measuring systems with a measuring transducer of the type being discussed have additionally surprisingly shown that suited as the wanted mode, especially also for ascertaining the mass flow rate as well as the density of the medium conveyed in the measuring transducer, is especially that natural oscillatory mode inherent to the tube arrangement—in the following referred to as the bending oscillation fundamental mode of the first type, or also as the V-mode oscillation—in which, as is also shown schematically in FIG. 7 a, the first measuring tube and the second measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane YZ, in each case about a static rest position associated with the respective measuring tube, and in which the third measuring tube and the fourth measuring tube execute bending oscillations which are likewise opposite-equal relative to the second imaginary longitudinal section plane, in each case about a static rest position associated with the respective measuring tube, and, indeed, in such a manner that—relative to the second imaginary longitudinal section plane YZ—said bending oscillations of the first measuring tube are also opposite-equal to said bending oscillations of the third measuring tube, and that—relative to the second imaginary longitudinal section plane YZ—said bending oscillations of the second measuring tube are also opposite-equal to said bending oscillations of the fourth measuring tube. The opposite-equal bending oscillations of the first and second measuring tubes or of the third and fourth measuring tubes in the V-mode here likewise formed as cantilever, bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes and causing the tube arrangement to appear in projection on the cross sectional plane XY at times V-shaped (compare FIG. 7 a))—are, in the case of a symmetrically constructed tube arrangement and a uniformly flowed-through tube arrangement, additionally symmetrically formed relative to the second imaginary longitudinal section plane YZ. The special suitability of the V-mode as the wanted mode for measuring transducers with four bent measuring tubes could, in such case, especially also be attributed especially to the resulting stress distribution in the measuring transducer (especially also in the region of the two flow dividers), which, in such case, is, as a whole, very favorable for the oscillatory behavior of the measuring transducer, considered both spatially as well as also in time, and can also be attributed to the equally favorable, and consequently very small, oscillation related deformations of the measuring transducer in general, as well as also of the flow dividers in particular.

Besides the aforementioned V-mode, the tube arrangement additionally also has a natural bending oscillation mode of a second type—referred to in the following as the X-mode—in which, as shown schematically in FIG. 7 b, the first measuring tube and the second measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane YZ about their respective associated static rest positions, and in which the third measuring tube and the fourth measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane YZ about their respective associated static rest positions, this contrasting with the bending oscillations in the V-mode, but in the manner, that, relative to the second imaginary longitudinal section plane YZ, said bending oscillations of the first measuring tube are also opposite-equal to said bending oscillations of the fourth measuring tube, and that, relative to the second imaginary longitudinal section plane YZ, said bending oscillations of the second measuring tube are also opposite-equal to said bending oscillations of the third measuring tube. In the case of symmetrically constructed and uniformly flowed through tube arrangements, moreover, also the bending oscillations in the X-mode (here, in turn, formed as cantilever, bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes and causing the tube arrangement to appear in projection on the cross sectional plane XY at times X-shaped (compare FIG. 7 b)) are likewise symmetric relative to the second imaginary longitudinal section plane YZ. In order to assure a separate, and especially also defined, exciting of the V-mode or of the X-mode over as broad as possible an operating range of the measuring transducer (characterized during operation by, among other things, fluctuating densities, mass flow rates, temperature distributions in the measuring transducer, etc.), according to an additional embodiment of the invention, the tube arrangement formed by means of the four measuring tubes, and consequently the measuring transducer formed therewith, is dimensioned in such a manner, that an eigenfrequency f_(18V,Ref) of the bending oscillation mode of the first type (V-mode), measurable, for example, in the case of a tube arrangement filled completely with air as a reference medium, is different from an eigenfrequency f_(18X,Ref) of the bending oscillation mode of the second type (X-mode) measurable especially in the case of a tube arrangement filled completely with air, or measurable at the same time as the eigenfrequency f_(18V,Ref) of the bending oscillation mode of the first type (V-mode), for example, such that the eigenfrequencies f_(18V,Ref), f_(18X,Ref) of the two mentioned bending oscillation modes (V-mode, X-mode) under the aforementioned reference conditions deviate from one another by 10 Hz or more. Especially also for the case of large nominal diameters of more than 150 mm, the tube arrangement is embodied in such a manner, that said eigenfrequency f_(18V,Ref) of the bending oscillation mode of the first type is more than 10 Hz greater than said eigenfrequency f_(18X,Ref) of the bending oscillation mode of the second type. The exciter mechanism is, according to an additional embodiment of the invention, consequently embodied in such a manner that, therewith, the first measuring tube 18 ₁ and the second measuring tube 18 ₂ are excitable during operation to opposite-equal bending oscillations, and the third measuring tube 18 ₃ and the fourth measuring tube 18 ₄ are excitable during operation to opposite-equal bending oscillations, especially also bending oscillations corresponding to the bending oscillation mode of the first type (V-mode) at its instantaneous eigenfrequency f_(18V), and bending oscillations corresponding to the bending oscillation mode of the second type (X-mode) at its instantaneous eigenfrequency f_(18V), the latter bending oscillations, in given cases, also occurring simultaneously with the bending oscillations corresponding to the bending oscillation mode of the first type (V-mode).

In an additional embodiment of the invention, the exciter mechanism 5 is formed by means of a first oscillation exciter 5 ₁ acting—especially differentially—on the first measuring tube 18 ₁, and by means of the second measuring tube 18 ₂, especially also for the purpose of exciting opposite-equal bending oscillations of the first and second measuring tube and/or of the third and fourth measuring tube. Additionally, it is provided that serving as first oscillation exciter 5 ₁ is an oscillation exciter of electrodynamic type, acting, especially differentially, on at least two of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄. Accordingly, the first oscillation exciter 5 ₁ is formed additionally by means of a permanent magnet held on the first measuring tube, and by means of a cylindrical coil held on the second measuring tube and permeated by the magnetic field of the permanent magnet, especially in the manner of a coil plunging arrangement, in the case of which the cylindrical coil is arranged coaxially with the permanent magnet, and the permanent magnet is embodied as an armature moving within the coil.

For the purpose of increasing the efficiency of the exciter mechanism and for the purpose of increasing the exciter forces generated therewith while simultaneously achieving a construction which is as symmetric as possible, in a further development of the invention, the exciter mechanism additionally comprises a second oscillation exciter 5 ₂ acting —especially electrodynamically and/or differentially—on the third measuring tube 18 ₃ and the fourth measuring tube 18 ₄. The second oscillation exciter 5 ₂ is advantageously embodied with equal construction to the first oscillation exciter 5 ₁, at least insofar as it works analogously to the latter's principle of action; thus, for example, it likewise is of electrodynamic type. In an additional embodiment, the second oscillation exciter 5 ₂ is consequently formed by means of a permanent magnet held on the third measuring tube, and a cylindrical coil held on the fourth measuring tube and permeated by the magnetic field of the permanent magnet. The two oscillation exciters 5 ₁, 5 ₂ of the exciter mechanism 5 can, in an advantageous manner, be electrically interconnected in series, especially in such a manner, that a common driver signal consequently excites simultaneous oscillations of the measuring tubes 18 ₁, 18 ₃, 18 ₂, 18 ₄; for instance, bending oscillations in the V-mode and/or in the X-mode. Particularly for the earlier mentioned case, in which both bending oscillations in the V-mode as well as also bending oscillations in the X-mode should be actively excited by means of the two oscillation exciters 5 ₁, 5 ₂, it can be of advantage to dimension the oscillation exciters 5 ₁, 5 ₂ in such a manner and to so place them on the tube arrangement in such a manner, that, as a result, a transmission factor of the first oscillation exciter 5 ₁, defined by a ratio of electrical excitation power fed thereinto to an exciter force effecting oscillations of the measuring tubes produced therewith, is different, at least within a frequency band including the V-mode and the X-mode, from a transmission factor of the second oscillation exciter 5 ₂, defined by a ratio of electrical excitation power fed thereinto to an exciter force effecting oscillations of the measuring tubes produced therewith, for instance, in such a manner, that said transmission factors deviate from one another by 10% or more. This enables, for example, also a separate exciting of V- and X-modes, especially also in the case of serial switching of the two oscillation exciter 5 ₁, 5 ₂ and/or supplying the two oscillation exciters 5 ₁, 5 ₂ with a single, shared driver signal, and can be achieved in the case of electrodynamic oscillation exciters 5 ₁, 5 ₂ in a very simple manner, e.g. by application of cylindrical coils with different impedances, or different numbers of windings and/or by differently dimensioned permanent magnets, or permanent magnets of different magnetic materials. It should here additionally be mentioned that, although the oscillation exciter or the oscillation exciters of the exciter mechanism shown here in the example of an embodiment in each case act, for instance, centrally on the respective measuring tubes, as an alternative to this or in supplementation thereof, oscillation exciters acting instead on the inlet and on the outlet sides of the particular measuring tube can also be used, for instance, in the manner of the exciter mechanisms proposed in U.S. Pat. No. 4,823,614, U.S. Pat. No. 4,831,885, or the US-A 2003/0070495.

As evident from FIGS. 2, 4 a, 4 b, 5 a and 5 b, and as is usual in the case of measuring transducers of the type being discussed, additionally provided in the measuring transducer 11 is a sensor arrangement 19, for example, an electrodynamic sensor arrangement, which reacts to vibrations of the measuring tubes 18 ₁, 18 ₂, 18 ₃, or 18 ₄, especially inlet and outlet-side vibrations, and especially bending oscillations excited by means of the exciter mechanism 5, this sensor arrangement serving for producing oscillation signals representing vibrations, especially bending oscillations, of the measuring tubes, and influenced—for example as regards a frequency, a signal amplitude and/or a phase position relative to one another and/or relative to the driver signal—by the measured variable to be registered, such as, for instance, the mass flow rate and/or the density and a viscosity of the medium, respectively.

In an additional embodiment of the invention, the sensor arrangement is formed by means of an inlet-side, first oscillation sensor 19 ₁ especially an electrodynamic, first oscillation sensor and/or a first oscillation sensor differentially registering at least oscillations of the first measuring tube 18 ₁ relative to the second measuring tube 18 ₂—as well as an outlet-side, second oscillation sensor 19 ₂—especially an electrodynamic, second oscillation sensor and/or a second oscillation sensor differentially registering at least oscillations of the first measuring tube 18 ₁ relative to the second measuring tube 18 ₂—wherein these two oscillation sensors respectively deliver a first and a second oscillation signal reacting to movements of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, especially their lateral deflections and/or deformations. This especially occurs in such a manner, that at least two of the oscillation signals delivered by the sensor arrangement 19 have a phase shift relative to one another, which corresponds to or depends on the instantaneous mass flow rate of the medium flowing through the measuring tubes, as well as, in each case, a signal frequency, which depends on an instantaneous density of the medium flowing in the measuring tubes. The two oscillation sensors 19 ₁, 19 ₂, which are, for example, equal to one another, can, for such purpose—as is quite usual in the case of measuring transducers of the type being discussed—be placed in the measuring transducer 11 essentially equidistantly from the first oscillation exciter 5 ₁. Moreover, the oscillation sensors of the sensor arrangement 19 can, at least insofar as they are of equal construction to the at least one oscillation exciter of the exciter mechanism 5, work analogously to the latter's principle of action, for example, thus likewise be of electrodynamic type. In a further development of the invention, the sensor arrangement 19 is additionally formed also by means of an inlet-side, third oscillation sensor 19 ₃—especially an electrodynamic oscillation sensor and/or an oscillation sensor differentially registering oscillations of the third measuring tube 18 ₃ relative to the fourth measuring tube 18 ₄—as well as an outlet-side, fourth oscillation sensor 19 ₄—especially an electrodynamic, fourth oscillation sensor 19 ₄ and/or an electrodynamic oscillation sensor differentially registering oscillations of the third measuring tube 18 ₃ relative to the fourth measuring tube 18 ₄. For additional improving of the signal quality, as well as also for simplifying the transmitter electronics 12 receiving the measurement signals, the first and third oscillation sensors 19 ₁, 19 ₃ can furthermore be electrically interconnected in series, for example, in such a manner, that a combined oscillation signal represents combined inlet-side oscillations of the first and third measuring tubes 18 ₁, 18 ₃ relative to the second and fourth measuring tubes 18 ₂, 18 ₄. Alternatively or in supplementation, the second and fourth oscillation sensors 19 ₂, 19 ₄ can also be electrically interconnected in series in such a manner, that a combined oscillation signal of both oscillation sensors 19 ₂, 19 ₄ represents combined outlet-side oscillations of the first and third measuring tubes 18 ₁, 18 ₃ relative to the second and fourth measuring tubes 18 ₂, 18 ₄.

For the aforementioned case, in which the oscillation sensors of the sensor arrangement 19, especially oscillation sensors constructed equally to one another, should differentially and electrodynamically register oscillations of the measuring tubes, the first oscillation sensor 19 ₁ is formed by means of a permanent magnet held to the first measuring tube—here in the region of oscillations to be registered on the inlet side—and a cylindrical coil permeated by the magnetic field of the permanent magnet and held to the second measuring tube—here correspondingly likewise in the region of oscillations to be registered on the inlet side; and the second oscillation sensor 19 ₂ is formed by means of a permanent magnet held—in the region of oscillations to be registered on the outlet side—to the first measuring tube and a cylindrical coil permeated by the magnetic field of the permanent magnet and held to the second measuring tube—here correspondingly likewise in the region of oscillations to be registered on the outlet side. Equally, additionally also the third oscillation sensor 19 ₃ in given cases provided can correspondingly be formed by means of a permanent magnet held to the third measuring tube and a cylindrical coil permeated by the magnetic field of the permanent magnet and held to the fourth measuring tube, and the fourth oscillation sensor 19 ₄ in given cases provided can be formed by means of a permanent magnet held to the third measuring tube and a cylindrical coil permeated by the magnetic field of the permanent magnet and held to the fourth measuring tube.

It is additionally to be noted here that, although, in the case of the oscillation sensors of the sensor arrangement 19 illustrated in the example of an embodiment, the oscillation sensor is, in each case, of electrodynamic type, and thus in each case formed by means of a cylindrical magnet coil affixed to one of the measuring tubes and a permanent magnet plunging therein and correspondingly affixed to an oppositely lying measuring tube, other oscillation sensors known to those skilled in the art, such as, for example, optoelectronic sensors, can additionally also be used for forming the sensor arrangement. Furthermore, as is quite usual in the case of measuring transducers of the type being discussed, in addition to the oscillation sensors, other sensors, especially auxiliary sensors or sensors registering disturbance variables, can be provided in the measuring transducer, such as, for example, acceleration sensors for registering movements of the total measuring system caused by external forces and/or asymmetries in the tube arrangement, strain gages for registering expansions of one or more of the measuring tubes and/or the transducer housing, pressure sensors for registering a static pressure reigning in the transducer housing and/or temperature sensors for registering temperatures of one or more of the measuring tubes and/or the transducer housing; by means of which, for example, the ability of the measuring transducer to function and/or changes in the sensitivity of the measuring transducer to the measured variables primarily to be registered (especially the mass flow rate and/or the density) as a result of cross sensitivities or external disturbances, can be monitored and, in given cases, correspondingly compensated for. For assuring as high as possible a sensitivity of the measuring transducer to the mass flow, according to an additional embodiment of the invention, the measuring tubes and the oscillation sensors are arranged in the measuring transducer in such a manner, that a measuring length, L₁₉, of the measuring transducer, corresponding to a separation between the first oscillation sensor 19 ₁ and the second oscillation sensor 19 ₂ measured along a deflection curve of the first measuring tube, amounts to more than 500 mm, especially more than 600 mm. Particularly for creating a measuring transducer which is as compact as possible, but nevertheless as sensitive as possible to the mass flow, according to an additional embodiment of the invention, the oscillation sensors 19 ₁, 19 ₂, matched to the installed length L₁₁ of the measuring transducer, are arranged in the measuring transducer in such a manner, that a measuring-length-to-installed-length ratio L₁₉/L₁₁ of the measuring transducer, which is defined by a ratio of the measuring length of the measuring transducer to the installed length, amounts to more than 0.3, especially more than 0.4 and/or less than 0.7. Alternatively or in supplementation, according to an additional embodiment of the invention, the oscillation sensors, matched to the measuring tubes, are placed in the measuring transducer in such a manner, that a caliber-to-measuring-length ratio D₁₈/L₁₉ of the measuring transducer, which is defined by a ratio of the caliber D₁₈ of the first measuring tube to the mentioned measuring length L₁₉ of the measuring transducer, amounts to more than 0.05, especially more than 0.09.

The sensor arrangement 19 is additionally, as is usual in the case of such measuring transducers, coupled in a suitable manner—for example, hardwired via connecting lines—with a measuring circuit correspondingly provided in the transmitter electronics; for example, a measuring circuit formed by means of at least one microprocessor and/or by means of at least one digital signal processor. The measuring circuit receives the oscillation signals of the sensor arrangement 19 and generates therefrom—in given cases also taking into consideration electrical excitation power fed by means of the at least one driver signal into the exciter mechanism, and consequently also converted therein—the previously mentioned measured values, which can represent, for example, a mass flow rate, a totalled mass flow and/or a density and/or a viscosity of the medium to be measured, and which, in given cases, can be displayed on-site and/or also sent in the form of digital measured data to a data processing system superordinated to the measuring system, and correspondingly further processed there. The measuring circuit, and consequently the transmitter electronics formed therewith, are especially additionally provided and designed to generate, based on electrical excitation power converted in the exciter mechanism, and, for example, in periodically recurring manner and/or on demand, a viscosity measured value representing the viscosity of the flowing medium, and/or, based on oscillation signals delivered by the measuring transducer, to generate, for example, in periodically recurring manner and/or on demand, a mass flow measured value representing the mass flow rate of the flowing medium, and/or, for example, in a periodically recurring manner and/or on demand, a density measured value representing the density of the flowing medium.

The above mentioned application of differentially acting oscillation exciters or oscillation sensors introduces, among other things, also the advantage, that for operating the measuring transducer of the invention, also such established measuring and operating circuits can be used as have already found broad application, for example, in conventional Coriolis mass flow and/or density measuring devices.

The transmitter electronics 12, including the measuring and operating circuits implemented therein, can furthermore be accommodated, for example, in a separate electronics housing 7 ₂, which is arranged removed from the measuring transducer, or, such as shown in FIG. 1, is affixed directly on the measuring transducer 1, for example, externally on the transducer housing 7 ₁, in order to form a single compact device. In the case of the example of an embodiment illustrated here, a neck-like transition piece serving for holding the electronics housing 7 ₂ is consequently additionally placed on the transducer housing 7 ₁. Within the transition piece can additionally be arranged a feedthrough for the electrical connecting lines between measuring transducer 11, especially the oscillation exciters and sensors placed therein, and the mentioned transmitter electronics 12. The feedthrough is manufactured so as to be hermetically sealed and/or pressure resistant, for example, by means of glass, and/or plastic potting compound.

As already mentioned several times, the measuring system, and thus also the measuring transducer 11, is provided especially also for measurements of high mass flows of more than 1000 t/h in a pipeline of large caliber of more than 250 mm. Taking this into consideration, according to an additional embodiment of the invention, the nominal diameter of the measuring transducer 11, which, as already mentioned, corresponds to a caliber of the pipeline, in whose course the measuring transducer 11 is to be used, is selected in such a manner, that it amounts to more than 50 mm, especially more than 100 mm. Additionally, according to a further embodiment of the measuring transducer, it is provided that each of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ in each case has a caliber D₁₈ corresponding to a particular tube inner diameter, which amounts to more than 40 mm. The measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are especially additionally embodied in such a manner, that each has a caliber D₁₈ of more than 60 mm. Alternatively or in supplementation thereof, the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are, according to another embodiment of the invention, additionally dimensioned in such a manner, that they in each case have a measuring tube length L₁₈ of at least 1000 mm. In the example of an embodiment illustrated here with equal-length measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, the measuring tube length L₁₈ in each case corresponds to a length of a section of the deflection curve of the first measuring tube extending between the first flow opening of the first flow divider and the first flow opening of the second flow divider. The measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are, in such case, especially designed in such a manner, that their measuring tube length L₁₈ is in each case greater than 1200 mm. At least for the mentioned case in which the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are composed of steel, in the case of the usually used wall thicknesses of over 1 mm, there accordingly in each case results an empty mass, M₁₈, of at least 20 kg, especially more than 30 kg. It is, however, desired that the empty mass of each of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ be kept smaller than 50 kg.

In consideration of the fact that, as already mentioned, in the case of the measuring transducer of the invention, each of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ weighs well over 20 kg, and, in such case, as is directly evident from the above dimensional specifications, can easily have a capacity of 10 l or more, the tube arrangement comprising the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ can then, at least in the case of a medium with high density flowing through, reach a total mass of far over 80 kg. Especially in the case of the application of measuring tubes with comparatively large caliber D₁₈, large wall thickness and large measuring tube length L₁₈, the mass of the tube arrangement formed by the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ can easily also be greater than 100 kg, or, at least with medium flowing through, e.g. oil or water, be more than 120 kg. As a result of this, an empty mass M₁₁ of the measuring transducer amounts, in total, also to far more than 200 kg, and, in the case of nominal diameters D₁₁ of significantly greater than 250 mm, even more than 300 kg. As a result, the measuring transducer of the invention can have a mass ratio M₁₁/M₁₈ of an empty mass M₁₁ of the total measuring transducer to an empty mass M₁₈ of the first measuring tube of easily greater than 10, especially greater than 15. In order, in the case of the mentioned high empty mass M₁₁ of the measuring transducer, to employ the total material used therefor as optimally as possible, and thus to utilize the—most often also very expensive—material as a whole as efficiently as possible, according to an additional embodiment, the nominal diameter D₁₁ of the measuring transducer is dimensioned relative to its empty mass M₁₁ in such a manner, that a mass-to-nominal-diameter ratio M₁₁/D₁₁ of the measuring transducer 11, as defined by a ratio of the empty mass M₁₁ of the measuring transducer 11 to the nominal diameter D₁₁ of the measuring transducer 11, is smaller than 2 kg/mm, and especially—to the greatest degree possible —smaller than 1 kg/mm. In order to assure a sufficiently high stability of the measuring transducer 11, the mass-to-nominal-diameter ratio M₁₁/D₁₁ of the measuring transducer 11 is, however, at least in the case of use of the above mentioned conventional materials, to be chosen so as to be to the greatest degree possible greater than 0.5 kg/mm. Additionally, according to an additional embodiment of the invention, for additional improvement of the efficiency of the installed material, the mentioned mass ratio M₁₁/M₁₈ is kept smaller than 25. For creation of a measuring transducer of sufficiently high oscillation quality factor which is nevertheless as compact as possible and has as little pressure drop as possible, according to an additional embodiment of the invention, the measuring tubes are dimensioned relative to the above mentioned installed length L₁₁ of the measuring transducer 11 in such a manner, that a caliber-to-installed-length ratio D₁₈/L₁₁ of the measuring transducer, as defined by a ratio of the caliber D₁₈ at least of the first measuring tube to the installed length L₁₁ of the measuring transducer 11, amounts to more than 0.02, especially more than 0.05 and/or less than 0.09, especially less than 0.07. Alternatively or in supplementation, the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are dimensioned relative to the above mentioned installed length L₁₁ of the measuring transducer in such a manner, that a measuring-tube-length-to-installed-length ratio L₁₈/L₁₁ of the measuring transducer, as defined by a ratio of the above-referenced measuring tube length L₁₈ at least of the first measuring tube to the installed length L₁₁ of the measuring transducer, amounts to more than 0.7, especially more than 0.8 and/or less than 1.2.

For the purpose of, on the one hand, improving the mechanical coupling of the four measuring tubes, along with an equalizing of the oscillations in the wanted mode simultaneously executed by the four measuring tubes also in the case of inequalities possibly caused by component tolerances, as well as, on the other hand, also for the purpose of an as simple as possible as well as effective implementing of a sufficient separating of the mentioned V-mode from the X-mode as regards their eigenfrequencies f_(18V), f_(18X)—thus, for example, in the mentioned order of magnitude of 10 Hz or more—the tube arrangement of the invention and consequently the measuring transducer formed therewith additionally comprises at least one first coupling element 24 ₁ of a first type for the adjusting the eigenfrequencies of natural oscillation modes the tube arrangement. The operation of said coupling element 24 ₁ of the first type can be explained in a simplified manner by stating that, in addition to bending stiffnesses, c₁₈, which are in each case inherent to the measuring tubes, and the eigenfrequencies of the oscillation modes the tube arrangement, especially also the of the V- and X-mode, other decisively co-determining bending or spring stiffnesses, c_(24V), c_(24X), which are namely inherent to the coupling element, have an effect within the tube arrangement. In such case, in an interesting aspect, said coupling element includes a decisively co-determining bending or spring stiffness, c_(24V), predominantly effective for the V-mode, and consequently for its eigenfrequency, f_(18V), wherein this bending or spring stiffness, c_(24V), is different from a decisively co-determining bending or spring stiffness, c_(24X), predominantly effective for the X-mode, and consequently its eigenfrequency, f_(18X), so that the coupling element thus adds mode-specific bending or spring stiffnesses, c_(24v), c_(24x), to the bending stiffnesses, c₁₈, of the measuring tubes, which are rather non-specific for the V- and the X-mode, and indeed almost the same, whereby, as a result, for the V- and the X-mode, equally specific bending or spring stiffnesses, 4c₁₈+c_(24V), 4c₁₈+c_(24X), are inherent to the tube arrangement as a whole.

The coupling element 24 ₁ of the first type is—as is also schematically presented in FIGS. 4 a through 9—affixed on each of the four measuring tubes spaced apart from both the first flow divider as well as also from the second flow divider, and, in the case of the measuring transducer of the invention, especially serves to set eigenfrequencies of such natural oscillation modes of the tube arrangement, in which each of the four measuring tubes in each case simultaneously executes or can execute bending oscillations about a particular static resting position. The coupling element 24 ₁ of first type is, according to an additional embodiment of the invention, additionally embodied and placed on the measuring tubes in such a manner, that it—as is also evident from the combination of FIGS. 4 a, 4 b, and 5 a, 5 b—is essentially symmetrical relative to the mentioned first imaginary longitudinal section plane XZ of the measuring transducer, or relative to the mentioned second imaginary longitudinal section plane YZ of the measuring transducer, and consequently the first imaginary longitudinal section plane XZ and/or the second imaginary longitudinal section plane YZ is thus in each case also a symmetry plane of the coupling element 24 ₁ of the first type.

The first coupling element of the first type includes a deformation body DB—in the example of an embodiment shown here, an essentially box-shaped deformation body DB formed by means of a frame construction having a plurality of profile struts or plates—as well as four connecting struts—which are here in each case formed by means of a bent rod or plate element, above all at least pairwise or also all essentially equally constructed—of which a first connecting strut V1 is connected with a first strut end with the deformation body and with a second strut end with the first measuring tube 18 ₁, a second connecting strut V2 is connected with a first strut end with the deformation body and with a second strut end with the second measuring tube, a third connecting strut V3 is connected with a first strut end with the deformation body and with a second strut end with the first measuring tube, and a fourth connecting strut V4 is connected with a first strut end with the deformation body and with a second strut end with the fourth measuring tube. In this regard, each of the four connecting struts V1, V2, V3, V4 thus in each case has a strut length defined by a minimum distance between their respective first strut ends and their respective second strut ends. In such cse, according to an additional embodiment of the invention, it is additionally provided to construct the connecting struts in such a manner, that both the second connecting strut as well as also the third, as well as the fourth connecting strut each have a strut length, which, in each case, is equal to the strut length, L_(V1), of the first connecting strut. The four connecting struts V1, V2, V3 and V4, which, are especially equally-constructed, can, for example, in each case be formed from the same material as or a similar material to the measuring tubes, consequently from a metal, for example, steel, and, for example, be produced from a simple, and in given cases also at least sectionally bent, flat rod.

To the total spring stiffness of the coupling element 24 ₁ of the first type, each of the four connecting struts V1, V2, V3, or V4 in each case contributes, among other things, a maximum bending stiffness, E_(V1)·J_(V1,max), E_(V2)·J_(V2,max), E_(V3)·J_(V3,max), or E_(V4)·J_(V4,max), about an imaginary bending principal axis in each case immanent to said longitudinal strut. The maximum bending stiffness of the particular connecting strut V1, V2, V3, or V4, is, in each case, determined by a modulus of elasticity, E_(V1), E_(V2), E_(V3), or E_(V4) dependent on the material of said connecting strut, as well as also on a respective minimum areal moment of inertia, J_(V1,max) J_(V2,max), J_(V3,max), or J_(V4,max), wherein, according to an additional embodiment of the invention, both the maximum areal moment of inertia of the second connecting strut as well as also the maximum areal moment of inertia of the third connecting strut and the maximum areal moment of inertia of the fourth connecting strut are in each case equal to the maximal areal moment of inertia, J_(V1,max), of the first connecting strut. Additionally, according to another embodiment of the invention, each of the four connecting struts V1, V2, V3, V4 is in each case arranged in such a manner, that the imaginary bending principal axis of their respective maximal areal moments of inertia in each case extends parallel both to the first longitudinal section plane XZ as well as also to the second imaginary longitudinal section plane YZ, and consequently, a contribution of the maximal bending stiffnesses of the connecting struts, at least to the bending or spring stiffnesses, 4c₁₈+c_(24v), 4c₁₈+c_(24x), of the coupling element 24 ₁ of the first type in each case effective for the eigenfrequencies of the V-mode and of the X-mode, is thus as large as possible.

Besides the maximal bending stiffness, each of the four connecting struts naturally in each case also has a minimal bending stiffness, E_(V1)·J_(V1,min), E_(V2)·J_(V2,min), E_(V3)·J_(V3,min), or E_(V4)·J_(V4,min), determined by the modulus of elasticity dependent on the respective material of said connecting strut, as well as also by a respective minimum areal moment of inertia, J_(V1,min), J_(V2,min), J_(V3,min), or J_(V4,min), about a imaginary bending principal axis in each case immanent to said connecting strut, wherein, according to an additional embodiment of the invention, each of the four connecting struts is in each case arranged in such a manner, that the imaginary bending principal axis of their respective minimum areal moments of inertia extends parallel to the first longitudinal section plane XZ and is perpendicular to the second imaginary longitudinal section plane YZ, and consequently, a contribution of the minimum bending stiffnesses of the connecting struts, at least to the bending or spring stiffnesses in each case effective for the eigenfrequencies of the V-mode and of the X-mode, 4c₁₈+c_(24v), 4c₁₈+c_(24x), of the coupling element 24 ₁ of first type is thus in each case negligibly small.

It is especially provided, as is also directly evident from the combination of FIGS. 4 a, 4 b, 4 c, 8 a, and 8 b, that each of the (especially equally constructed) connecting struts of the coupling element 24 ₁ of the first type is at least sectionally straight—and, for example, also predominantly straight, or, as is schematically presented in the FIGS. 4 a, 4 b, 4 c, 8 a, and 8 b, completely straight—in projection on the imaginary cross sectional plane XY, and/or that each of the connecting struts of the coupling element of the first type extends at least sectionally perpendicular to the first imaginary longitudinal section plane XZ, and consequently parallel to the second imaginary longitudinal section plane YZ. For the mentioned case, in which each of the connecting struts of the coupling element of the first type has a straight subsection, which extends perpendicular to the first imaginary longitudinal section plane XZ, and consequently parallel to the second imaginary longitudinal section plane YZ, according to an additional embodiment of the invention, it is additionally provided that—as is also evident from the combination the FIGS. 4 a, 4 b, 4 c, 8 a, and 8 b—the first and the third connecting struts are aligned flush with one another and the second and fourth connecting strut aligned flush with one another, and/or that each of the connecting struts of the coupling element of the first type imaginarily intersects the first imaginary longitudinal section plane XZ, especially with the mentioned respective straight subsection, and for example, at an angle of as close to exactly 90° as possible.

According to an additional embodiment of the invention, the deformation body of the coupling element—in the example of an embodiment shown here, formed virtually as a box or frame construction, or as an interconnection of struts—at least two longitudinal struts—here equally constructed, plate-shaped longitudinal struts—of which a first longitudinal strut L1 extending from the first connecting strut to the third connecting strut, especially an at least sectionally straight first longitudinal strut L1, as well as a second longitudinal strut L2 extending from the second connecting strut to the fourth connecting strut, especially an at least sectionally straight second longitudinal strut L2, or one constructed equally to the first longitudinal strut. The first longitudinal strut L1 is in such case arranged, spaced apart from the second imaginary longitudinal section plane YZ, exclusively on a side of said longitudinal section plane YZ occupied both by the first as well as also by the third measuring tube, while the second longitudinal strut L2 is arranged, spaced apart from the second imaginary longitudinal section plane YZ, especially by the same distance as the first longitudinal strut, exclusively on a side of said longitudinal section plane YZ occupied both by the second as well as also by the fourth measuring tube.

Each of the two longitudinal struts in each case contributes to the total spring stiffness of the coupling element 24 ₁ of first type, among other things, a minimal bending stiffness, E_(L1)·J_(L1,min) or E_(L1)·J_(V1,min), about an imaginary bending principal axis in each case immanent said longitudinal strut, as well as a spring stiffness, c_(L1), or c_(L12), for a tension or compressive force in each case acting on said longitudinal strut, in each case, directed perpendicularly to the first imaginary longitudinal section plane XZ. The minimal bending stiffness of the particular longitudinal strut is, in each case, determined by an modulus of elasticity, E_(L1), or E_(L2), dependent on a material of said longitudinal strut, as well as also by a particular minimum areal moment of inertia, J_(L1,min), or J_(L2,min), while the spring stiffness is determined by the particular modulus of elasticity, E_(L1), or E_(L2), as well as also by the particular strut length, l_(L1) or l_(L2), as well as a particular surface area, A_(L1), or A_(L2), of a cross sectional area of the particular longitudinal strut in each case coincident with the first imaginary longitudinal section plane XZ, especially in such a manner, that the spring stiffness, c_(L1), of the first longitudinal strut behaves proportionally to the relationship E_(L1)·A_(L2)/l_(L1), and the spring stiffness, c_(L2), of the second longitudinal strut behaves proportionally to the relationship E_(L2)·A_(L2)/l_(L2). According to an additional embodiment of the invention, the first longitudinal strut and the second longitudinal strut are additionally embodied and arranged in such a manner, that the minimal bending stiffness, E_(L1)·J_(L1,min), of the first longitudinal strut is equal to the minimum bending stiffness, E_(L2)·J_(L2,min), of the second longitudinal strut, or that the spring stiffness, c_(L1), of the first longitudinal strut is equal to the spring stiffness, c_(L2), of the second longitudinal strut.

For the purpose of implementing as simple a construction of the coupling element as possible, each of the two longitudinal struts is additionally in each case advantageously embodied in such a manner, that they are at least sectionally straight—and especially predominantly or completely straight—in projection on the mentioned imaginary cross sectional plane XY of the tube arrangement, and/or that they at least sectionally extend perpendicular to the mentioned first imaginary longitudinal section plane XZ, and consequently parallel to the mentioned second imaginary longitudinal section plane YZ. According to an additional embodiment of the invention, each of the two longitudinal struts L1 consequently in each case has a subsection, which is straight at least in projection on the imaginary cross sectional plane XY, wherein this subsection, in projection on said cross sectional plane XY, in the case of the first longitudinal strut, extends with a length, l_(L1), extending between the first and third connecting strut, or in the case of the second longitudinal strut, with a length, l_(L2), extending between the second and fourth connecting strut, perpendicular to the first imaginary longitudinal section plane XZ at least in projection on the imaginary cross sectional plane XY, and extends—in the case the first longitudinal strut at a distance of a_(L1) or in the case the second longitudinal strut at a distance of a_(L2)—parallel to the second imaginary longitudinal section plane YZ. In such case, it has additionally been shown that, for the purpose of achieving a contribution of the longitudinal struts to the total spring stiffness of the coupling element 24 ₁ of the first type sufficient for the desired separating of the eigenfrequencies of the V- and of the X-mode of the tube arrangement, the distance, a_(L1), of first longitudinal strut L1 or the distance, a_(L2), of second longitudinal strut from the second imaginary longitudinal section plane YZ should in each case amount to more than 50% of the outer diameter, D₁₈+2·h₁₈, of the first measuring tube or of the four measuring tubes, but can, however, amount to far less than 200% of said outer diameter, D₁₈+2·h₁₈.

As is evident from the combination of FIGS. 4 a, 4 b, 4 c, 8 a, 8 b, in the example of an embodiment shown here, the two longitudinal struts L1, L2 are additionally embodied in such a manner, that in each case, practically the entire longitudinal strut is straight at least in projection on the imaginary cross sectional plane XY, that the straight subsection of the first longitudinal strut thus extends from the first connecting strut up to the third connecting strut, and consequently its length, l_(L1), corresponds to a minimum distance between the first strut end of the first connecting strut and the first strut end of the third connecting strut, or the straight subsection of the second longitudinal strut extends from the second connecting strut up to the fourth connecting strut, and consequently its length, l_(L2), corresponds to a minimum distance between the first strut end of the first second connecting strut and the first strut end of the fourth connecting strut. Furthermore, in the example of an embodiment shown here, the straight subsection of the first longitudinal strut L1 is the same distance from the first imaginary longitudinal section plane XZ as the straight subsection of the second longitudinal strut L1 is, so that the distance, a_(L1), which the first longitudinal strut extends parallel to the second imaginary longitudinal section plane YZ is equal to the distance, a_(L2), which the second longitudinal strut extends parallel to said longitudinal section plane YZ, or the straight subsection of the first longitudinal strut is the same length as the straight subsection of the second longitudinal strut, so that the length, l_(L1), with which the straight subsection of the first longitudinal strut extends between the first and third connecting strut, is equal to the length, l_(L2), with which the straight subsection of the second longitudinal strut extends between the first and third connecting strut. Further investigations have additionally shown that a strut length for the connecting struts or for the longitudinal struts optimal for the desired separating of the V-mode from the X-mode with respect to their eigenfrequencies f_(18V), f_(18X), lies in a region, in which the specification:

${\frac{1_{V\; 1}}{1_{V\; 1} + {0.5 \cdot I_{L\; 1}}} > 0.3},$

as well as also the specification:

$\frac{1_{V\; 1}}{1_{V\; 1} + {0.5 \cdot I_{L\; 1}}} < 0.7$

are fulfilled. Moreover, for the coupling element 24 ₁ of the first type, especially good results can be achieved, both as regards the separating of the V-mode from the X-mode as well as also as regards an effective mechanical coupling of the four measuring tubes, when the coupling element 24 ₁ is dimensioned with respect to the measuring tubes in such a manner, that, as a result, the tube arrangement, as a whole, fulfills both the specification:

$\frac{1_{V\; 1} + {0.5 \cdot 1_{L\; 1}}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} > 0.2$

as well as also the specification

${\frac{1_{V\; 1} + {0.5 \cdot 1_{L\; 1}}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} < 0.9},$

or when the deformation body DB of the coupling element 24 ₁ is dimensioned with respect to the measuring tubes in such a manner, that the tube arrangement, as a result, fulfills both the specification:

$\frac{0.5 \cdot 1_{L\; 1}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} > 0.1$

as well as also the specification:

$\frac{0.5 \cdot 1_{L\; 1}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} < {0.5.}$

In such case, the two longitudinal struts L1, L2, which are especially equally constructed, can, for example, be formed from the same material as or a similar material to the measuring tubes or the connecting struts—consequently from a metal, for example steel—and, for example, can be produced from a simple flat rod. Moreover, the two longitudinal struts are advantageously arranged and oriented in the measuring transducer in such a manner, that they in each case imaginarily intersect—for example, with the mentioned straight subsection—the first imaginary longitudinal section plane XZ, for instance, in the manner shown in FIGS. 4 a, 4 b, 4 c, or 8 a, 8 b, namely in each case at an angle of 90°.

Particularly also for the mentioned case, in which the eigenfrequency, f_(18V) of the V-mode should be set lower than the eigenfrequency, f_(18X), of the X-mode, according to an additional embodiment of the invention, the first longitudinal strut and the second longitudinal strut are arranged in such a manner, that both the mentioned imaginary bending principal axis of the minimal areal moment of inertia, J_(L1,min), of the first longitudinal strut, as well as also the imaginary bending principal axis of the minimal areal moment of inertia, J_(L2,min), of the second longitudinal strut in each case extend parallel both to the first longitudinal section plane XZ as well as also to the second imaginary longitudinal section plane YZ, and consequently a contribution of the minimum bending stiffnesses of the longitudinal struts at least to the bending or spring stiffnesses, 4c₁₈+c_(24v), 4c₁₈+4c_(24x), of the coupling element 24 ₁ of the first type in each case effective for the eigenfrequencies of the V-mode and of the X-mode, is in each case as large as possible. Moreover, a high effectiveness of the coupling element 24 ₁ of the first type in the sense of the desired separating of the eigenfrequencies, f_(18V), f_(18X), of the V and X-mode can be achieved when the maximum bending stiffness, E_(v1)·J_(V1,max), of first connecting strut V1, and consequently also that of the second, third and fourth connecting strut V2, V3, or V4, is in each case selected so as to be greater than the minimal bending stiffness, E_(L1)·J_(L1,min), of the first longitudinal strut, especially, when the first coupling element or the tube arrangement formed therewith, fulfills, as a result, the specification

$\frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{E_{L\; 1} \cdot J_{{L\; 1},\min}} > 5.$

Alternatively or in supplementation, as is furthermore evident from the combination of FIGS. 4 a, 4 b, 4 c, 8 a, 8 b, and 9, the two longitudinal struts are, in the shown example of an embodiment, additionally arranged in such a manner, that an imaginary bending principal axis, which is in each case immanent to each of the longitudinal struts, and is associated with a maximal bending stiffness, E_(L1)·J_(L1,max), or E_(L1)·J_(L2,max), of the particular longitudinal strut, in each case extends parallel to the first imaginary longitudinal section plane XZ and perpendicular to the second imaginary longitudinal section plane YZ, and consequently, a contribution of the maximal bending stiffnesses of the longitudinal struts at least to the bending or spring stiffnesses, 4c₁₈+c_(24v), 4c₁₈+c_(24x), of the coupling element 24 ₁ of the first type in each case effective for the eigenfrequencies of the V-mode and of the X-mode is in each case negligibly small. The maximum bending stiffness, E_(L1)·J_(L1,max), or E_(L1)·J_(L2,max), is in each case determined by a maximal areal moment of inertia, J_(L1,max), or J_(L2,max), of the particular longitudinal strut about the respective associated imaginary bending principal axis, as well as, in turn, by the modulus of elasticity, E_(L1), or E_(L2). In an advantageous manner, the maximal bending stiffnesses, E_(L1)·J_(L1,max) or E_(L1)·J_(L2,max), for each of the two longitudinal struts L1, L2, are, in each case, additionally dimensioned in such a manner so as to be equally large.

According to an additional embodiment of the invention, the deformation body DB further includes a first cross brace Q1, especially an at least sectionally straight first cross brace Q1 and/or one sectionally extending non-parallel to the second imaginary longitudinal section plane YZ, here, for example, extending perpendicular. As is directly evident from the combination of FIGS. 4 a, 4 b, 4 c, 8 a, and 8 b, the first cross brace Q1, which is, for example, manufactured from the same material as connecting struts V1, V2, V3, V4 and/or longitudinal struts L1, L2, extends, in such case, from the first connecting strut to the second connecting strut, here, for example, in such a manner, that it also reaches from the first longitudinal strut L1 up to the second longitudinal strut L2. In such case, in the example of an embodiment shown here, both the first connecting strut as well as also the second connecting strut are in each case affixed with their respective first strut ends directly on the first cross brace Q1. Like the connecting struts or the longitudinal struts, the first cross brace can also be formed, for example, by means of a flat rod, which, for instance, is made of metal, and consequently composed of the same material as or a similar material to the connecting struts or the longitudinal struts. Like the two longitudinal struts L1, L2, the cross brace Q1 also produces a bending stiffness corresponding to the total spring stiffness of the coupling element 24 ₁ of the first type, and especially a minimal bending stiffness, E_(Q1)·J_(Q1,min), about an imaginary bending principal axis immanent to said cross brace Q1, wherein said minimal bending stiffness, E_(Q1)·J_(Q1,min), in turn, is determined by a modulus of elasticity, E_(Q1), dependent on the material said cross brace Q1, as well as also by a respective minimum areal moment of inertia, J_(Q1,min), of said cross brace Q1. According to an additional embodiment of the invention, the cross brace Q1 is, in such case, additionally arranged in such a manner, that the imaginary bending principal axis of its minimal areal moment of inertia, J_(Q1,min), extends parallel both to the first longitudinal section plane XZ as well as also to the second imaginary longitudinal section plane YZ, for example in such a manner, that (as is shown in FIGS. 4 a, 4 b, 4 c, 8 a, or 8 b) said imaginary bending principal axis lies in the second imaginary longitudinal section plane YZ. Moreover, cross brace Q1 is also additionally oriented in such a manner, that an imaginary bending principal axis associated with a maximum bending stiffness, E_(Q1)·J_(Q1,max), of the cross brace Q1 extends perpendicular to the first imaginary longitudinal section plane XZ and extends parallel to the second imaginary longitudinal section plane YZ, wherein the maximum bending stiffness, E_(Q1)·J_(Q1,max), is determined by a maximal areal moment of inertia, J_(Q1,max), about said imaginary bending principal axis, and, in turn, by the modulus of elasticity, E_(Q1). As a result of this, a contribution of the maximal bending stiffness of the cross strut Q1 at least on the bending or spring stiffnesses, 4c₁₈+c_(24v), 4c₁₈+c_(24x), of the coupling element 24 ₁ of the first type in each case effective for the eigenfrequencies of the V-mode and of the X-mode, is thus, in turn, negligibly small.

In the case of the example of an embodiment shown here with a coupling element 24 ₁ of the first type having a rather box-shaped deformation body, said deformation body furthermore includes a second cross brace Q2, extending—here in a manner equivalent to the first cross brace Q1—from the first longitudinal strut to the second longitudinal strut, and, consequently, for example, at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane YZ and/or constructed equally to the first cross brace, wherein this second cross brace Q2, like the first cross brace Q1, can likewise be formed by means of a flat rod—for instance, one made from metal—and wherein this second cross brace Q2 namely likewise contributes to the total spring stiffness of the coupling element 24 ₁, especially to a degree equivalent to the first cross brace Q1 of the first type, a minimal bending stiffness, E_(Q2)·J_(Q2,min), about an imaginary bending principal axis immanent to said cross brace Q2, wherein said minimal bending stiffness, E_(Q2)·J_(Q2,min), is in turn determined by the modulus of elasticity, E_(L1), as well as also of a respective minimum areal moment of inertia, J_(Q2,min), of said cross brace Q1. According to an additional embodiment of the invention, the first and second cross braces are additionally in each case arranged in such a manner, that, in each case, the imaginary bending principal axis of their respective minimal areal moments of inertia, J_(Q1,min), or J_(Q2,min), respectively, in each case extend parallel both to the first longitudinal section plane XZ as well as also to the second imaginary longitudinal section plane YZ, and consequently, a contribution of the minimum bending stiffnesses of the cross braces Q1, Q2 at least to the bending or spring stiffnesses, 4c₁₈+c_(24v), 4c₁₈+c_(24x), of the coupling element 24 ₁ of the first type in each case effective for the eigenfrequencies of the V-mode and of the X-mode, is thus in each case as large as possible. The cross struts can, in such case, also be arranged, for example, in such a manner, that, as is shown in FIGS. 4 a, 4 b, 4 c, 8 a, or 8 b, each of the two imaginary bending principal axes in each case lies in the second imaginary longitudinal section plane YZ. Advantageously, the first cross brace Q1 and the second cross brace Q2 can furthermore each be composed of the same material and/or each be composed of steel.

For the purpose of additional improving of the effectiveness of the separating of the eigenfrequency of the V-mode of the tube arrangement from that of the X-mode desired by the invention, according to an additional embodiment of the invention, the deformation body includes, in addition to the first and second longitudinal struts, also at least one other longitudinal strut, which extends from the first cross brace to the second cross brace with a length, l_(L3), and is straight in projection on the imaginary cross sectional plane XY, namely a third longitudinal strut L3. The third longitudinal strut, as is schematically presented in FIGS. 4 a, 4 b, or 4 c or 8 a, 8 b, is affixed with a first strut end on the first cross brace, as well as with a second strut end lying opposite the first on the second cross brace, and, in the example of an embodiment shown here, in a region in which the first cross brace Q1 or the second cross brace in each case imaginarily intersects the second imaginary longitudinal section plane YZ. The third longitudinal strut L3 can, for example, also be plate-shaped, or be formed by means of a corresponding flat rod, for instance, one made of the same material as the two other longitudinal struts L1, L2 and/or the two cross braces Q1, Q1, for example, made of steel. In a further embodiment of the invention, the length, l_(L3), of the third longitudinal strut L3 is additionally selected so as to be greater than 10% of the length, l_(L1), of the first longitudinal strut L1, or smaller than 120% of the length, l_(L1), of first longitudinal strut L1. For example, the longitudinal strut L3—as is also evident from the combination of FIGS. 4 a, 4 b, 4 c, 8 a, 8 b—can, for instance, be embodied so as to have a length equal to that of the two other longitudinal struts L1, L2.

For the case shown here, in which the deformation body is formed by means of an uneven number on longitudinal struts, said third longitudinal strut L3 is additionally arranged in such a manner, that it is in each case spaced equally far apart from the first longitudinal strut L1 and from the second longitudinal strut L2. As a result of this, in the present example of an embodiment, the third longitudinal strut L3 contributes a further spring stiffness, c_(L3), for a tension or compressive force acting on said longitudinal strut L3 and directed perpendicular to the first imaginary longitudinal section plane XZ, wherein this spring stiffness, c_(L3,min), behaves essentially proportional to a specification E_(L3)·A_(L3)/l_(L3), and consequently is determined by a modulus of elasticity, E_(L3), dependent on the material of said longitudinal strut L3, as well as also by its length, l_(L3), as well as by a surface area, A_(L3), of a cross sectional area coincident with the first imaginary longitudinal section plane XZ. Additionally, also the third longitudinal strut L3 can advantageously be arranged in such a manner, that an imaginary bending principal axis associated with a minimum bending stiffness, E_(L3)·J_(L3,min), inherent to said longitudinal strut L3 extends parallel both to the first imaginary longitudinal section plane XZ as well as also to the second imaginary longitudinal section plane YZ, or that an imaginary bending principal axis associated with a maximal areal moment of inertia, J_(L3,max), inherent to said longitudinal strut L3 extends parallel to the first imaginary longitudinal section plane XZ and perpendicular to the second imaginary longitudinal section plane YZ. In such case, the minimal bending stiffness, E_(L3)·J_(L3,min), of the third longitudinal strut L3 is, in turn, dependant on the modulus of elasticity, E_(L3), predetermined by its material, as well as also dependent on a minimum areal moment of inertia, J_(L3,min), about the imaginary bending principal axis associated with this, while, in addition to the modulus of elasticity, E_(L3), a maximum areal moment of inertia, J_(L3,max), about said imaginary bending principal axis associated with the maximal bending stiffness, E_(L3)·J_(L3,max), determines the maximum bending stiffness, E_(L3)·J_(L3,max).

Particularly also for the mentioned case, in which the eigenfrequency, f_(18V), of the V-mode should be set lower than the eigenfrequency, f_(18X), of the X-mode, according to an additional embodiment of the invention, the first, second and third longitudinal struts are additionally each dimensioned in such a manner and arranged relative to one another in such a manner, that, as a result, the deformation body DB, and consequently the coupling element, 24 ₁, of first type formed therewith, or the tube arrangement formed therewith, fulfills the specification:

${\frac{{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \frac{E_{L\; 1} \cdot A_{L\; 1}}{l_{L\; 1}}} + {\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}}}{6 \cdot \frac{E_{L\; 1} \cdot J_{{L\; 1},\min}}{l_{L\; 1}}} > 1},$

or the specification:

$\frac{{\left( \frac{a_{L\; 2}}{2} \right)^{2} \cdot \frac{E_{L\; 2} \cdot A_{L\; 2}}{l_{L\; 2}}} + {\left( \frac{a_{L\; 2}}{2} \right)^{2} \cdot \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}}}{6 \cdot \frac{E_{L\; 2} \cdot J_{{L\; 2},\min}}{l_{L\; 2}}} > 1.$

Additionally, the deformation body should, in comparison to the connecting struts, be dimsensioned in such a manner, that, as a result, the coupling element 24 ₁ of first type fulfills the specification:

$\frac{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \left( {\frac{E_{L\; 1} \cdot A_{L\; 1}}{l_{L\; 1}} + \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}} \right)}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} > 2.$

As a result of further investigations, it has additionally been shown, that the coupling element 24 ₁ of first type is optimal for the desired separating of the eigenfrequency, f_(18V), of the V-mode of the eigenfrequency, f_(18X), the X-mode, when fulfills it the specification

$\frac{\frac{1}{l_{V\; 1}^{2}}\left\lbrack {\frac{1}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} + \frac{1}{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \left( {\frac{E_{L\; 1} \cdot A_{L\; 1}}{l_{L\; 1}} + \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}} \right)}} \right\rbrack}{\frac{1}{l_{V\; 1}^{2}} \cdot \left\lbrack {\frac{1}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} + \frac{1}{6 \cdot \frac{E_{L1} \cdot J_{{L\; 1},\min}}{l_{L\; 1}}}} \right\rbrack} > 1.$

Moreover, further investigations have shown it to be very advantageous, when—as indicated in FIG. 4 a, 4 b, or 4 c, or 8 a, 8 b—the first cross brace Q1 has a smaller cross section, and consequently a smaller—here also minimal—areal moment of inertia, J_(Q1,min), in a region, in which this first cross brace Q1 imaginarily intersects the second imaginary longitudinal section plane YZ, than it has in an adjoining, neighboring region extending to the first connecting strut V1, and than it has in an adjoining, neighboring region extending to the second connecting strut V2; or the second cross brace Q2 has a smaller cross section, and consequently smaller—here namely also minimal—areal moment of inertia, J_(Q2,min), in a region in which this imaginarily intersects the second imaginary longitudinal section plane YZ, than it has in an adjoining, neighboring region extending to the third connecting strut V3, and than it has in an adjoining, neighboring region extending to the fourth connecting strut V4; and when—in the mentioned case of the use of an uneven number of longitudinal struts of the aforementioned type for forming the coupling element 24 ₁—the third longitudinal strut L3 is affixed its the first strut end on the first cross brace Q1 in said region of the latter's minimum areal moment of inertia, J_(Q1,min), and is affixed with its second strut end on the second cross brace Q2 in the region of the latter's minimum areal moment of inertia, J_(Q2,min). As a result of this, the contribution of the two cross braces Q1, Q2 to the spring stiffness, c_(24v), of the coupling element 24 ₁ of the first type predominantly effective for the V-mode, and consequently to the spring stiffness, 4c₁₈+c_(24v), determining the eigenfrequency of the V-mode of the tube arrangement as a whole, can, for example, be lessened relative to the contribution, which the two cross braces Q1, Q2 make to the spring stiffness, c_(24X), of the coupling element 24 ₁ of the first type predominantly effective for the X-mode, and consequently to the spring stiffness, 4c₁₈+c_(24X), determining the eigenfrequency of the X-mode of the tube arrangement as a whole.

Naturally inherent to the coupling element 24 ₁ of the first type are a plurality of natural eigenmodes, some of which can also exhibit a certain meaning for a dimensioning of the coupling element, which is optimal as regards the desired separating of the eigenfrequencies of the V-mode and of the X-mode of the tube arrangement. For example, the coupling element 24 ₁ of the first type shown in each of FIGS. 4 a, 4 b, 4 c, or 8 a, 8 b-which is embodied as a frame construction—can have an eigenmode of a first type, in which the deformation body of said coupling element executes mechanical oscillations in a coupler plane or plane of oscillation XY₁ parallel to the imaginary cross sectional plane KY with an eigenfrequency, f_(24X), wherein these oscilltions—as is also schematically presented in FIG. 8 a—are mirror symmetrical both relative to the first imaginary longitudinal section plane YZ as well as also relative to the second imaginary longitudinal section plane YZ, or which allow the deformation body to appear mirror symmetrical both relative to the first imaginary longitudinal section plane YZ as well as also relative to the second imaginary longitudinal section plane YZ. Additionally, said coupling element 24 ₁ can additionally have an additional eigenmode, namely an eigenmode of a second type, in which the deformation body of said coupling element can execute mechanical oscillations in said coupler plane XY₁ parallel to the imaginary cross sectional plane XY with an eigenfrequency, f_(24V), most often different from the eigenfrequency, f_(24X), of the eigenmode of first type—wherein these oscillations—as is schematically presented in FIG. 8 b—are mirror symmetrical only relative to the second imaginary longitudinal section plane YZ, or allow the deformation body temporarily to appear mirror symmetrical only relative to the second imaginary longitudinal section plane YZ.

In such case, as is evident from the combination of FIGS. 7 a, 7 b, 8 a, 8 b, the eigenmode of the first type inherent to the coupling element 24 ₁ corresponds with the X-mode of the tube arrangement, and the eigenmode of the second type inherent to the coupling element 24 ₁ corresponds with the V-mode of the tube arrangement as regards their respective oscillatory movements. Recognizing this, according to an additional embodiment of the invention, the deformation body, and consequently the coupling element formed therewith is additionally dimensioned in such a manner, that an eigenfrequency ratio, f_(24X)/f_(24V), inherent to said coupling element, this eigenfrequency ratio being defined by a ratio of the eigenfrequency of its eigenmode of the first type to the eigenfrequency of its eigenmode of the second type, is greater than one, and, to the greatest degree possible, also greater than 10. As a result of this, a spring stiffness ratio inherent to the coupling element 24 ₁, this spring stiffness ratio being defined by a ratio of a spring stiffness, c_(24X), co-determining the eigenfrequency, f_(24X), of its eigenmode of the first type, and consequently also co-determining the eigenfrequency of the X-mode of the entire tube arrangement, to a spring stiffness, c_(24V), co-determining the eigenfrequency, f_(24V), of its eigenmode of the second type, and consequently also co-determining the eigenfrequency of the V-mode of the entire tube arrangement, is greater than one, or ideally also greater than 10.

For the case, in which the coupling element 24 ₁ of the first type essentially corresponds to a combination of previously individually described solutions for specific details, not least of all, however, also the construction resulting from from the combination of FIGS. 4 a, 4 b, 4 c, 5 a, 5 b as well as 8 a, 8 b, the spring stiffness, c_(24X), predominantly effective for the X-mode can be estimated, moreover with quite good accuracy, via the relationship

${{\frac{1}{l_{V\; 1}^{2}} \cdot \left\lbrack {\frac{1}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} + \frac{1}{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \left( {\frac{E_{L\; 1} \cdot A_{L\; 1}}{l_{L\; 1}} + \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}} \right)}} \right\rbrack} \approx c_{24\; x}},$

while the spring stiffness, c_(24V), of the coupling element 24 ₁ of first type predominantly effective for the V-mode corresponds in good approximation to the relationship:

${\frac{1}{l_{V\; 1}^{2}} \cdot \left\lbrack {\frac{1}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} + \frac{1}{6 \cdot \frac{E_{L1} \cdot J_{{L\; 1},\min}}{l_{L\; 1}}}} \right\rbrack} \approx {c_{24\; v}.}$

Further investigations on pipe arrangements according to the present invention have additionally yielded the result, that other natural oscillation modes of the coupling element of importance for operation of a measuring transducer of the invention can be such an eigenmode of the coupling element 24 ₁, in which the deformation body can oscillate with a respective eigenfrequency about an associated static rest position in such a manner, that simultaneously thereto, also the four connecting struts execute bending oscillations about a particular static resting position, in the direction of the longitudinal axis. Of particular interest in such case, is, for example, also that eigenmode of the coupling element 24 ₁—here designated the eigenmode of the third type—in which the deformation body, moving essentially only translationally in the direction of a longitudinal axis parallel both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane—here thus also the longitudinal axis L—can oscillate with an eigenfrequency, f_(24Z), about an associated static rest position, and namely can do in such a manner, that the four connecting struts essentially uniformly (or essentially in the same direction) execute bending oscillations about a particular static resting position in the direction the said longitudinal axis. Recognizing this, according to an additional embodiment of the invention, the coupling element of the first type is additionally embodied in such a manner, that the eigenfrequency, f_(24Z), of its eigenmode of the third type is not equal to the mentioned eigenfrequency, f_(18V,Ref), of the bending oscillation mode of the first type of the tube arrangement, measurable in the case of measuring tubes completely filled with air. In such case, it has proved especially advantageous when, for example, said eigenfrequency, f_(24Z), of the coupling element of the first type is greater than said eigenfrequency, f_(18V,Ref), of the V-mode of the tube arrangement by more than 10 Hz, or when said eigenfrequency, f_(24Z), of the coupling element of the first type amounts to more than 101%—and, to the greatest degree possible, more than 105%—of said eigenfrequency, f_(18V,Ref), of the V-mode the tube arrangement. Of further interest can additionally, for example, also be that eigenmode of the coupling element 24 ₁—here designated the eigenmode of the fourth type—in which the deformation body, moving only translationally in the mentioned coupler plane or plane of oscillation XY₁, can oscillate with an eigenfrequency, f_(24XY), about its associated static rest position, and can do so in such a manner, that the four connecting struts uniformly (and/or in the same direction) execute bending oscillations about their respective static resting positions in the coupler plane XY₁. For preventing undesired disturbing influences, also that eigenfrequency, f_(24XY′), of the eigenmode of the fourth type of the coupling element 24 ₁ should, in turn, be set so as to be higher than the eigenfrequency, f_(18X), of the bending oscillation mode of the second type of the tube arrangement, and, to the greatest degree possible in such a manner, that said eigenfrequency, f_(24XY′), of the mode of oscillation of the fourth type of the coupling element first type is greater than said eigenfrequency, f_(18X), of the X-mode of the tube arrangement by more than 10 Hz, and/or that said eigenfrequency, f_(24XY′), of the mode of oscillation of fourth type of the coupling element of first type amounts to more than 101%—and, to the greatest degree possible, more than 105%—of said eigenfrequency, f_(18X), of the X-mode the tube arrangement.

For the purpose of preventing disturbing influences potentially generated on the part of the coupling element of the first type—for instance, in one of the aforementioned eigenmodes of the coupling element of the first type on an eigenfrequency of the actively excited wanted mode, and consequently of the V-mode—the deformation body DB of the coupling element of first type—formed here, for example, by means of three longitudinal struts L1, L2, L3 and two cross braces Q1, Q2—is, according to an additional embodiment of the invention, dimensioned in such a manner, that it has a mass, M_(DB), which amounts to less than 50% of the empty mass, M₁₈, of first measuring tube. Additionally, the connecting struts, which are especially equally-constructed, as well as the deformation body DB affixed thereto, which in given cases, also a has a mass, M_(DB), amounting to more than 10% of the empty mass, M₁₈, of the first measuring tube, is, according to an additional embodiment of the invention, dimensioned in such a manner, that said coupling element 24 ₁ also fulfills the specification:

${\frac{\sqrt{\frac{1}{M_{VK}} \cdot \frac{E_{V1} \cdot J_{{V\; 1},\min}}{l_{V\; 1}^{3}}}}{f_{{18\; V},{Ref}}} > 1.05},$

that a frequency value,

$\sqrt{\frac{1}{M_{VK}} \cdot \frac{E_{V1} \cdot J_{{V\; 1},\min}}{l_{V\; 1}^{3}}},$

at least approximately corresponding to an eigenfrequency of the coupling element 24 ₁, thus amounts to more than 105% of the above mentioned eigenfrequency, f_(18X,Ref), of the V-mode, measurable in the case of a tube arrangement completely filled with air.

If required—for example, because the measuring transducer is provided for measuring extremely hot media or for measuring in applications with operating temperatures fluctuating over a broad range, for instance, as a result of cleaning procedures of the measuring transducer recurringly performed in-situ (“cleaning in process”, “sterilizing in process” etc.), and, in this respect, notable thermal expansions of the measuring tubes are to be expected—the coupling element 24 ₁ of the first type can additionally be embodied in such a manner, that it can expand in a manner essentially equal to that of the measuring tubes in each case coupled thereover, and/or that it is sufficiently flexible at least relative to forces, which extend in the direction of a line of action through the peaks of the two measuring tubes connected with one another by the particular coupling elements of second type; for instance, coincident with or parallel to the mentioned imaginary vertical axis V. This can, as investigations on pipe arrangements of the invention have shown, be achieved directly, by the tube arrangement as a whole fulfilling the specification:

$\frac{\frac{E_{V\; 1} \cdot A_{V\; 1}}{l_{V\; 1}}}{3 \cdot \frac{E_{18} \cdot J_{18}}{a_{K}^{3} \cdot \left( {1 - {1.5 \cdot \frac{a_{k}}{L_{18\; x}}}} \right)}} < 20.$

As a result of this, a temperature working range for a measuring transducer according to the present invention quite sufficient for a large number of industrial application cases, namely a temperature working range extending over more than 50 K (Kelvin), and consequently the measuring system formed therewith, can be provided. The flexibility of the coupling element in the direction of the vertical axis V can—alternatively or in supplementation to the implementation of the aforementioned specification with the tube arrangement—in a simple as well as very effective manner, for example, via the already mentioned application of a curved flat rod for the connecting struts, which, in projection on the second imaginary longitudinal section plane YZ, is, for example, at least sectionally S-shaped, Z-shaped, V-shaped, and/or—as is schematically presented in FIG. 5 a, 5 b-decidedly V-shaped. In such case, it can additionally nevertheless be quite advantageous, not least of all also for the purpose of implementing a coupling element sufficiently effective for the desired separating of the eigenfrequencies of the V-mode and of the X-mode of the tube arrangement, to construct the connecting struts—as is also evident from the combination of FIGS. 4 a, 4 b, 4 c, 5 a, 5 b—so as to be curved only in projection on the second imaginary longitudinal section plane YZ, but not, however, in projection on the cross sectional plane XY, or on the first imaginary longitudinal section plane XZ. Thus, on the one hand, a small change in the relative separation, for instance as a result of thermally caused strain, between measuring tubes can be enabled, and indeed in a manner largely preventing increases of mechanical stresses within the tube arrangement negatively influencing the oscillatory behavior of the tube arrangement; however, on the other hand, a sufficient separating of the eigenfrequencies of the V-mode and of the X-mode of the tube arrangement can also be achieved. The aforementioned curvature of the connecting struts visible in projection on the second imaginary longitudinal section plane YZ can additionally advantageously be embodied in such a manner, that each of the connecting struts, as is also indicated in FIGS. 4 a, 4 b, 5 a, 5 b, are in each case at least sectionally convex relative to the imaginary cross sectional plane XY, namely as viewed from the cross sectional plane XY.

Particularly for the mentioned case, and consequently that shown by way of example in FIGS. 4 a, 4 b, 4 c, 5 a, 5 b, in which the first coupling element 24 ₁, of the first type is arranged spaced apart from the cross sectional plane Xy, here namely on the inlet side in the measuring transducer, according to a further development, the tube arrangement moreover comprises a second coupling element 24 ₂ of the first type for setting eigenfrequencies of natural oscillation modes of the tube arrangement, not least of all also the eigenfrequencies of the V-mode and of the X-mode of the tube arrangement, wherein this second coupling element 24 ₂ of the first type is affixed—here on the outlet side—on each of the four measuring tubes, spaced apart both from the first flow divider as well as also from the second flow divider, as well as also from the first coupling element 24 ₁, of the first type, and is especially essentially constructed equally to the first coupling element 24 ₁ of the first type. For the already mentioned case, in which the first coupling element 24 ₁, of the first type is placed in the measuring transducer on the inlet side, and the second coupling element 24 ₂ of the first type is placed in the measuring transducer on the outlet side, the two mentioned coupling elements 24 ₁, 24 ₂ of the first type are, according to an additional embodiment of the invention, additionally also arranged in the measuring transducer symmetrically relative to the mentioned imaginary cross sectional plane XY of the measuring transducer, and consequently equidistantly relative to said cross sectional plane XY, and extending parallel relative to said cross sectional plane XY at least with their respective deformation bodies.

Furthermore, if required, mechanical stresses and/or vibrations possibly or at least potentially caused at the inlet side or at the outlet side in the transducer housing by the relatively large-dimensioned measuring tubes vibrating especially in the mentioned manner can, for example, be minimized by mechanically connecting the four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ with one another at least pairwise on the inlet side and on the outlet side, in each case by means of coupling elements serving as so-called node plates, in the following referred to as coupling elements of second type. Moreover, by means of such coupling elements of the first type, be it through their dimensioning and/or their positioning on the measuring tubes, mechanical eigenfrequencies of the measuring tubes, and thus also mechanical eigenfrequencies of the tube arrangement formed by means of the four measuring tubes (including additional components of the measuring transducer placed thereon), and consequently also the natural eigenfrequencies of its V-mode and its X-mode, respectively, and thus also the oscillatory behavior of the measuring transducer as a whole, can be targetedly influenced. The coupling elements of second type serving as node plates can, for example, be thin plates or washers, manufactured especially from the same material as or a similar material to the measuring tubes, which, in each case, corresponding with the number and the outer dimensions of the measuring tubes to be coupled with one another, are provided with bores, and, in given cases, supplementally slitted to the edge, so that the washers can first be mounted onto the respective measuring tubes 18 ₁, 18 ₂ and 18 ₃, 18 ₄, and, in given cases, thereafter still be bonded to the respective measuring tubes; for example, by hard soldering or welding.

Accordingly, in an additional embodiment of the invention, the tube arrangement comprises a first coupling element 25 ₁ of the second type, for example, a plate shaped first coupling element 25 ₁ of the second type, which (as is directly evident from FIGS. 4 a, 4 b, 5 a, 5 b, 6 a), for forming inlet-side oscillation nodes at least for vibrations—especially also bending oscillations, for instance, those in the mentioned V-mode—of the first measuring tube, and for vibrations of the second measuring tube opposite-equal thereto, is affixed on the inlet side to the first measuring tube and to the second measuring tube, and is spaced apart from the first flow divider; as well as a second coupling element 25 ₂ of the second type, which is, for instance, constructed equally to the first coupling element, and which, for forming outlet-side oscillation nodes for vibrations—especially also bending oscillations, thus those in the mentioned V-mode or X-mode —of the first measuring tube 18 ₁ and for vibrations of the second measuring tube 18 ₁ opposite-equal thereto, is affixed on the outlet side to the first measuring tube 18 ₁ and to the second measuring tube 18 ₂, and spaced apart from the second flow divider 20 ₂. Equally, the tube arrangement includes, for forming inlet-side oscillation nodes for vibrations especially the mentioned bending oscillations—of the third measuring tube and for vibrations of the fourth measuring tube opposite-equal thereto, a third coupling element 25 ₃ of the second type, which is, for instance, again plate shaped, and/or constructed equally to the first coupling element 24 ₁ of the second type, and which is affixed on the inlet side to the third measuring tube and to the fourth measuring tube, and apart spaced from the first flow divider, as well as, for forming outlet-side oscillation nodes for vibrations—for instance, the mentioned bending oscillations—of the third measuring tube and for vibrations of the fourth measuring tube opposite-equal thereto, a fourth coupling element 25 ₄ of the second type, which is, for instance, constructed equally to the first coupling element 25 ₁ of the second type, and which is affixed on the outlet side to the third measuring tube and to the fourth measuring tube and spaced apart from the second flow divider.

In an additional embodiment of the invention, the four aforementioned coupling elements 25 ₁, 25 ₂, 25 ₃, 25 ₄ of the second type are, as is also directly evident from the combination of FIGS. 4 a, 4 b, 5 a, 5 b, 6 a, 6 b, in each case affixed to exactly two of the four measuring tubes—but not otherwise to any other of the four measuring tubes—so that, as a result, the first and second coupling elements 25 ₁, 25 ₂ of second the type are affixed only to the first and second measuring tubes, and the third and fourth coupling element 25 ₃, 25 ₄ of the second type are affixed only to the third and fourth measuring tubes. As a result of this, the tube arrangement, and consequently also the measuring transducer, can be manufactured, for example, in a manner such that, first, the first and second coupling elements 25 ₁, 25 ₂ of the second type are in each case affixed to the (future) first and second measuring tubes 18 ₁, 18 ₂ for forming a first measuring tube package, and the third and fourth coupling elements 25 ₃, 25 ₄ of the second type are in each case affixed to the (future) third and fourth measuring tubes 18 ₃, 18 ₄ for forming a second measuring tube package. It is then possible to add the two measuring tube packages at a later point in time to the tube arrangement, for instance, directly before or also after insertion of the two measuring tube packages into the mentioned tubular middle segment 7 _(1A) of the (future) transducer housing, by correspondingly affixing the first and second coupling elements 24 ₁, 24 ₂ of the first type to each of the two measuring tube packages, for instance, for the time being, in each case to at least one of the measuring tubes 18 ₁, 18 ₂ of the first measuring tube package, and to at least one of the measuring tubes 18 ₃, 18 ₄ of the second measuring tube package. This has—especially also for the mentioned case, in which the measuring transducer is designed for large nominal diameters of more than 100 mm, in spite of the relatively large dimensions of its components, and consequently of the tube arrangement, of the transducer housing, of the flow dividers, etc.—the advantage, that the tube arrangement, which, as a result, is relatively spread-out, needs to be handled as a totality only at a relatively late point in the time of the total manufacturing process. Moreover, this permits use of long existant, conventional measuring transducer technology for double tube arrangements, which brings about a considerable reducing of the manufacturing and inventory costs. If required, the coupling elements 25 ₁, 25 ₂, 25 ₃, 25 ₄ can, however, also in each case be affixed in a corresponding manner to all four measuring tubes, for example also in the case, in which the measuring transducer is designed for relatively small nominal diameters of 50 mm or less.

In the example of an embodiment shown here, the first coupling element 25 ₁ of the second type is affixed both to a—here sectionally bent —inlet-side tube segment of the first measuring tube 18 ₁ extending between the first flow divider 20 ₁ and the first coupling element 24 ₁ of the first type as well as also to an inlet-side tube segment of the second measuring tube 18 ₂ likewise extending between the first flow divider 20 ₁ and the first coupling element 24 ₁ of the first type, and the second coupling element 25 ₂ of the second type is affixed both to a —here likewise sectionally bent—outlet-side tube segment of the first measuring tube 18 ₁ extending between the second flow divider 20 ₂ and the second coupling element 24 ₂ of the first type as well as also to an outlet-side tube segment of the second measuring tube 18 ₂ likewise extending between the second flow divider 20 ₂ and the second coupling element 24 ₂ of the first type. In an analogous manner, the third coupling element 25 ₃ of the second type is affixed both to a—here likewise sectionally bent—inlet-side tube segment of the third measuring tube 18 ₃ extending between the first flow divider 20 ₁ and the first coupling element 24 ₁ of the first type, as well as also to an inlet-side tube segment of the fourth measuring tube 18 ₄ likewise extending between the first flow divider 20 ₁ and the first coupling element 24 ₁ of the first type, and the fourth coupling element 25 ₄ of the second type is affixed both to a—here, again, sectionally bent—outlet-side tube segment of the third measuring tube 18 ₃ extending between the second flow divider 20 ₂ and the second coupling element 24 ₂ of the first type as well as also to an outlet-side tube segment of the fourth measuring tube 18 ₄ likewise extending between the second flow divider 20 ₂ and the second coupling element 24 ₁ of the first type. This especially occurs in such a manner, that—as is directly evident from the combination of FIGS. 4 a, 4 b, 5 a, 5 b—at least the first and fourth coupling elements of the second type are parallel to one another, and at least the second and third coupling elements of the second type are parallel to one another. Each of the four aforementioned coupling elements 25 ₁, 25 ₂ of the second type—which are especially constructed equally to one another—is, according to an additional embodiment of the invention, additionally embodied so as to be plate shaped, for example in such a manner, that it in each case has a rectangular basic shape, or, as is shown in FIGS. 4 a, 4 b, has a more oval basic shape. As is additionally evident from the combination of FIGS. 4 a, 4 b, 5 a, 5 b, the four coupling elements 24 ₁, 24 ₂ 24 ₃, 24 ₄ can additionally be embodied in such a manner and placed in the measuring transducer in such a manner, that they are arranged symmetrically relative to the imaginary longitudinal section plane YZ, and pairwise symmetrically relative to the imaginary longitudinal section plane XZ and relative to the imaginary cross sectional plane XY. As a result, a center of mass of each of the coupling elements of the second type thus in each case has the same distance from a center of mass of the tube arrangement. In the context of a still simpler and still more exact adjusting of the oscillatory behavior of the measuring transducer, it can additionally be quite advantageous when the measuring transducer moreover has—as, for example, is provided in US-A 2006/0150750 and as is indicated in FIGS. 4 a, 4 b, 5 a, 5 b—still other coupling elements of the aforementioned type acting as node plates, for example, a total of 8 or 12 coupling elements of the second type.

As is schematically presented in FIGS. 5 a and 5 b, the tube form of each of the measuring tubes, together with a minimum distance between the first and second coupling elements of the second type—and consequently thus in the case of application of 8 or more such coupling elements, the coupling elements of the second type lying on the inlet and outlet sides which are in each case nearest the center of mass of the tube arrangement, and thus, in this respect, the coupling elements of the second type lying innermost on the inlet and outlet sides—in each case define a wanted oscillatory length, L_(18x), of each of the measuring tubes. The wanted oscillatory length, L_(18x), of the particular measuring tubes corresponds, in such case—as is also schematically presented in FIGS. 5 a and 5 b—to a length of the section of the bent line of said measuring tube extending between the two coupling elements 25 ₁, 25 ₂ of the second type, wherein, according to an additional embodiment of the invention, the coupling elements of the second type are placed in the measuring transducer in such a manner, that, as a result, the wanted oscillatory length of each of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ amounts to less than 3000 mm, especially less than 2500 mm and/or more than 800 mm. Alternatively or in supplementation, it is additionally provided to construct the measuring tubes and to arrange the coupling elements of the first type in such a manner, that all four measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ have, as a result, the same wanted oscillatory length, L_(18x). According to an additional embodiment of the invention, the first measuring tube and the second measuring tube, at least in the region extending between the first coupling element of the second type and the second coupling element of the second type—consequently thus in their respective wanted oscillatory lengths—are additionally parallel to one another, and also the third measuring tube and the fourth measuring tube, at least in the region extending between the third coupling element of the second type and the fourth coupling element of the second type—and consequently thus their respective wanted, oscillatory lengths—are parallel to one another.

As is evident from the combination of FIGS. 4 a, 4 b, 5 a, and 5 b, the first coupling element of the first type and the first or third coupling element of the second type are additionally arranged in such a manner, that a minimal distance between the first coupling element of the second type and the second end of the second connecting strut of the coupling element of the first type, measured along a surface element of the second measuring tube, is equal to a minimum distance, a_(K), between the first coupling element of the second type and the second end of the first connecting strut of the coupling element of the first type, measured along a surface element of the first measuring tube, and that both a minimal distance between the third coupling element of the second type and the second end of the third connecting strut of the coupling element of the first type, measured along a surface element of the third measuring tube, as well as also a minimal distance between the third coupling element of the second type and the second end of the fourth connecting strut of the coupling element of the first type, measured along a surface element of the fourth measuring tube, is in each case equal to the minimum distance, a_(K), between the first coupling element of the second type and the second end of the first connecting strut of the coupling element of the first type.

Further investigations with pipe arrangements according to the present invention have additionally yielded the result, that it can be advantageous, for instance also for the purpose of minimizing the deforming influence of the coupling element of the first type on the original natural oscillation form of the measuring tubes, when the first coupling element 24 ₁, matched to the measuring tubes, and not least of all also to the maximal lateral expansion Q₁₈ of the tube arrangement resulting from its shape and arrangement, or matched the tube cross sections of the measuring tubes, is dimensioned in such a manner and is affixed by means of its connecting struts on the measuring tubes in such a manner, that the tube arrangement, as a result, fulfills the specification:

${\frac{0.5 \cdot l_{L\; 1}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} \leq {\frac{a_{k}}{L_{18,x}} + \frac{{0.5 \cdot D_{18}} + h_{18} + {0.5 \cdot A_{18}}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)}}},$

or also the specification:

$\frac{0.5 \cdot l_{L\; 1}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} > {{0.2 \cdot \frac{a_{k}}{L_{{18,x}\;}}} + {\frac{{0.5 \cdot D_{18}} + h_{18} + A_{18}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)}.}}$

For the purpose of additional improving of the effectiveness, with which, by means of the coupling element of the first type, the desired separating of the eigenfrequencies, f_(18V), f_(18X), of the V- and X-mode of the tube arrangement ultimately is achieved, as an alternative to or in supplementation of the preceding specification, the measuring tubes and the coupling element 24 ₁ of the first type are, according to an additional embodiment of the invention, additionally embodied or arranged in such a manner, that the tube arrangement formed therewith, as a result, fulfills the specification

${\left. \frac{c\; 24\; x}{c\; 18} \right.\sim\frac{\frac{1}{l_{V\; 1}^{2}} \cdot \left\lbrack {\frac{1}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} + \frac{1}{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \left( {\frac{E_{L\; 1} \cdot A_{L\; 1}}{l_{L\; 1}} + \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}} \right)}} \right\rbrack}{3 \cdot \frac{E_{18} \cdot J_{18}}{a_{K}^{3} \cdot \left( {1 - {1.5 \cdot \frac{a_{k}}{L_{18\; x}}}} \right)}}} > {0.01.}$

For creation of as compact as possible a measuring transducer of sufficiently high oscillation quality factor and high sensitivity coupled with as little a pressure drop as possible, according to an additional embodiment of the invention, the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are dimensioned, matched to the mentioned, wanted oscillatory length, in such a manner, that a caliber-to-oscillatory-length ratio D₁₈/L_(18x) of the measuring transducer, defined by a ratio of the caliber D₁₈ of the first measuring tube to the wanted oscillatory length L_(18x) of the first measuring tube, amounts to more than 0.03, especially more than 0.05 and/or less than 0.15. As an alternative to this or in supplementation thereof, according to an additional embodiment of the invention, the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄ are dimensioned, matched to the above-mentioned installed length L₁₁ of the measuring transducer, in such a manner, that an oscillatory-length-to-installed-length ratio L_(18x)/L₁₁ of the measuring transducer, defined by a ratio of the wanted oscillatory length L_(18x) of the first measuring tube to the installed length L₁₁ of the measuring transducer, amounts to more than 0.55, especially more than 0.6 and/or less than 1.5. According to an additional embodiment of the invention, the oscillation sensors are arranged in the measuring transducer, matched to the wanted oscillatory length, in such a manner, that a measuring-length-to-oscillatory-length ratio L₁₉/L_(18x) of the measuring transducer, defined by a ratio of the mentioned measuring length L₁₉ of the measuring transducer to the wanted oscillatory length L_(18x) of the first measuring tube, amounts to more than 0.3, especially more than 0.4 and/or less than 0.95. Moreover, the measuring length, L₁₉, and/or measuring-length-to-oscillatory-length ratio L₁₉/L_(18x) can, moreover, also be more exactly determined according to criteria proposed in the assignee's non-pre-published international applications PCT/EP2010/058797 and PCT/EP2010/058799 for determining optimum measuring lengths or optimum measuring-length-to-oscillatory-length ratios for measuring transducers of vibration type.

For lessening possible cross sensitivities of the measuring transducer to pressure, especially also in the case of as high as possible a nominal-diameter-to-installed-length ratio D₁₁/L₁₁ of more than 0.1 and as low as possible an oscillatory-length-to-installed-length ratio L_(18x)/L₁₁ of less than 1.5, annular stiffening elements additionally can be used on the measuring tubes, wherein each of these annular stiffening elements is placed on exactly one of the measuring tubes 18 ₁, 18 ₂, 18 ₃, 18 ₄, in such a manner, that it encompasses the latter along one of its—especially circularly orbiting—imaginary peripheral lines; compare to this also the previously mentioned U.S. Pat. No. 6,920,798. It can, in such case, especially be of advantage, when at least four such stiffening elements, especially equally constructed stiffening elements, are placed on each of the measuring tubes 18 ₁, 18 ₂, 18 ₃, or 18 ₄. In such case, the stiffening elements can, for example, be placed in the measuring transducer 11 in such a manner, that two adjoining stiffening elements mounted on the same measuring tube have a separation from one another, which amounts to at least 70% of a pipe outer diameter of said measuring tube, but at most amounts to 150% of such pipe outer diameter. In such case, a separation of neighboring stiffening elements from one another which lies in the range of 80% to 120% of the pipe-outer diameter of the respective measuring tube 18 ₁, 18 ₂, 18 ₃, or 18 ₄ has proved especially suitable.

Through application of four bent measuring tubes flowed-through in parallel—instead of, as hitherto been the case, two such measuring tubes—it is then also possible in a cost-effective manner to manufacture measuring transducers of the described type also for large mass flow rates, or with large nominal diameters of far over 250 mm, on the one hand having an accuracy of measurement of over 99.8% at an acceptable pressure drop, especially of less than 3 bar, and, on the other hand, keeping the installed mass, as well as also the empty mass, of such measuring transducers sufficiently within limits, so that, in spite of large nominal diameter, manufacture, transport, installation, as well as also operation can still always occur in an economically sensible manner. Especially also via implementation—individually or also in combination—of the above explained measures for further developing the invention, measuring transducers of the type being discussed can also, in the case of large nominal diameters, be embodied in such a manner and dimensioned in such a manner, that a mass ratio of the measuring transducer, as defined by a ratio of the mentioned empty mass of the measuring transducer to a total mass of the tube arrangement, can readily be kept smaller than 3, especially smaller than 2.5. 

1. A measuring transducer of the vibration type for registering at least one physical, measured variable of a flowable medium conveyed in a pipeline, especially a gas, a liquid, a powder or other flowable material, and/or for producing Coriolis forces serving for registering a mass flow rate of a flowable medium, especially a gas, a liquid, a powder or other flowable material, conveyed in a pipeline, the measuring transducer comprises: a transducer housing—especially an at least partially essentially tubular and/or at least partially externally circularly cylindrical transducer housing—of which an inlet-side, first housing end is formed by means of an inlet-side, first flow divider having exactly four, mutually spaced apart flow openings, especially circularly cylindrical, tapered or conical flow openings, and an outlet-side, second housing end formed by means of an outlet-side, second flow divider having exactly four, mutually spaced apart flow openings, especially circularly cylindrical, tapered or conical flow openings; a tube arrangement having four curved or bent (especially at least sectionally V-shaped or at least sectionally circular arc-shaped), measuring tubes, which are connected to said flow dividers, especially equally constructed flow dividers, for guiding flowing medium along flow paths connected in parallel, especially four measuring tubes held oscillatably in said transducer housing only by means of said flow dividers, and/or which are equally constructed and/or pairwise parallel relative to one another, of which a first measuring tube opens with an inlet-side, first measuring tube end into a first flow opening of said first flow divider, and with an outlet-side, second measuring tube end into a first flow opening of said second flow divider, a second measuring tube, especially one at least sectionally parallel to said first measuring tube, opens with an inlet-side, first measuring tube end into a second flow opening of said first flow divider and with an outlet-side, second measuring tube end into a second flow opening of said second flow divider, a third measuring tube opens with an inlet-side, first measuring tube end into a third flow opening of said first flow divider and with an outlet-side, second measuring tube end into a third flow opening of said second flow divider, a fourth measuring tube, especially one at least sectionally parallel to said third measuring tube, opens with an inlet-side, first measuring tube end into a fourth flow opening of said first flow divider and with an outlet-side, second measuring tube end into a fourth flow opening of said second flow divider; a first coupling element of a first type, which is spaced apart both from said first flow divider as well as also from said second flow divider, which is affixed, especially on the inlet side, on each of said four measuring tubes, which is especially embodied as a frame construction and/or as an interconnection of struts, and which serves for setting eigenfrequencies of natural oscillation modes of the tube arrangement, especially such, in which each of said four measuring tubes simultaneously executes or can execute bending oscillations about a particular static resting position; an electro-mechanical exciter mechanism, especially one formed by means of an electro-dynamic, first oscillation exciter, and/or a first oscillation exciter differentially exciting oscillations of said first measuring tube relative to said second measuring tube, and by means of an electro-dynamic, second oscillation exciter, and/or a second oscillation exciter differentially exciting oscillations of said third measuring tube relative to said fourth measuring tube, and/or a second oscillation exciter constructed equally to said first oscillation exciter, for producing and/or maintaining bending oscillations each of said four measuring tubes, especially bending oscillations corresponding to a natural bending oscillation mode of the tube arrangement, wherein said two flow dividers are embodied and arranged in the measuring transducer in such a manner, that an imaginary first connecting axis of the measuring transducer imaginarily connecting said first flow opening of said first flow divider with said first flow opening of said second flow divider extends parallel to an imaginary second connecting axis of the measuring transducer imaginarily connecting the second flow opening of said first flow divider with said second flow opening of said second flow divider, and that a imaginary third connecting axis of the measuring transducer imaginarily connecting said third flow opening of said first flow divider with said third flow opening of said second flow divider extends parallel to an imaginary fourth connecting axis of the measuring transducer imaginarily connecting said fourth flow opening of said first flow divider with said fourth flow opening of said second flow divider, wherein the measuring tubes are embodied and arranged in such a manner, that the tube arrangement has a first imaginary longitudinal section plane extending both between said first measuring tube and said third measuring tube, as well as also between said second measuring tube and said fourth measuring tube, and that the tube arrangement has a second imaginary longitudinal section plane perpendicular to its imaginary first longitudinal section plane and extending both between said first measuring tube and said second measuring tube as well as also between said third measuring tube and said fourth measuring tube, wherein: said first coupling element of the first type has a deformation body, especially one which is box-shaped and/or formed by means of a frame construction having a plurality of profile struts and/or plates, as well as four connecting struts, which are especially equally long and/or at least pairwise equally constructed; of which a first connecting strut, which is especially rod or plate-shaped, and which is connected with a first strut end with the deformation body, and with a second strut end with said first measuring tube; a second connecting strut, which is especially rod or plate-shaped, and which is connected with a first strut end with the deformation body and with a second strut end with said second measuring tube; a third connecting strut, which is especially rod or plate-shaped, and which is connected with a first strut end with the deformation body and with a second strut end with said first measuring tube; and a fourth connecting strut, which is especially rod or plate-shaped, and which is connected with a first strut end with the deformation body and with a second strut end with said fourth measuring tube.
 2. The measuring transducer as claimed in claim 1, wherein: said exciter mechanism is embodied in such a manner, that each of said four measuring tubes is excitable, especially simultaneously, to bending oscillations; and/or said exciter mechanism is embodied in such a manner, that said first measuring tube and said second measuring tube are excitable to bending oscillations opposite-equal relative to said second imaginary longitudinal section plane, especially bending oscillations symmetric relative to said second imaginary longitudinal section plane, and said third measuring tube and said fourth measuring tube are excitable to bending oscillations opposite-equal relative to said second imaginary longitudinal section plane, especially bending oscillations symmetric relative to the second imaginary longitudinal section plane; and/or said exciter mechanism is embodied in such a manner, that said first measuring tube and said third measuring tube are excitable to bending oscillations opposite-equal relative to the second imaginary longitudinal section plane, especially bending oscillations symmetric relative to the second imaginary longitudinal section plane, and said second measuring tube and said fourth measuring tube are excitable to bending oscillations to bending oscillations opposite-equal relative to the second imaginary longitudinal section plane, especially bending oscillations symmetric relative to the second imaginary longitudinal section plane (YZ).
 3. The measuring transducer as claimed in claim 1, wherein: the tube arrangement is mirror symmetrical relative to said first imaginary longitudinal section plane.
 4. The measuring transducer as claimed in claim 1, wherein: the tube arrangement is mirror symmetrical relative to the second imaginary longitudinal section plane.
 5. The measuring transducer as claimed in claim 1, wherein: the tube arrangement is mirror symmetrical both relative to the first imaginary longitudinal section plane as well as also relative to the second imaginary longitudinal section plane.
 6. The measuring transducer as claimed in claim 1, wherein: said coupling element of the first type is embodied and arranged in such a manner, that it is mirror symmetrical both relative to the first imaginary longitudinal section plane (XZ) as well as also relative to the second imaginary longitudinal section plane of the tube arrangement.
 7. The measuring transducer as claimed in claim 1, wherein: each of said four measuring tubes in each case has a bending stiffness determined by a modulus of elasticity dependent on a material of said measuring tube, as well as also by an areal moment of inertia dependent on a caliber and a wall thickness; and both said second measuring tube as well as also said third measuring tube and said fourth measuring tube in each case have a bending stiffness, which in each case is equal to a bending stiffness, E₁₈·J₁₈, of said first measuring tube.
 8. The measuring transducer as claimed in claim 1, wherein: said deformation body is formed by means of a frame construction, especially one having a plurality of profile struts and/or plates.
 9. The measuring transducer as claimed in claim 1, wherein: the tube arrangement has an imaginary cross sectional plane in each case perpendicular both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane.
 10. The measuring transducer as claimed in claim 9, wherein: a center of mass of the tube arrangement lies in the imaginary cross sectional plane; and/or wherein: the tube arrangement is mirror symmetrical relative to the imaginary cross sectional plane; and/or wherein: each of the four measuring tubes in each case has a measuring tube-peak, defined as greatest perpendicular distance of the respective measuring tube from the first imaginary longitudinal section plane, and the imaginary cross sectional plane intersects each of the four measuring tubes in its respective measuring tube peak.
 11. The measuring transducer as claimed in claim 9, wherein: inherent to the coupling element of the first type is an eigenmode of a first type, in which the deformation body of said coupling element can execute mechanical oscillations with an eigenfrequency, f_(24X), in a plane of oscillation parallel to the imaginary cross sectional plane, wherein these oscillations are mirror symmetrical both relative to the first imaginary longitudinal section plane as well as also relative to the second imaginary longitudinal section plane, or cause said deformation body to appear mirror symmetrical both relative to the first imaginary longitudinal section plane as well as also relative to the second imaginary longitudinal section plane, wherein: inherent to said coupling element of the first type is an eigenmode of a second type, in which said deformation body of said coupling element can execute mechanical oscillations in said plane of oscillation parallel to the imaginary cross sectional plane with an eigenfrequency, which is especially different from the eigenfrequency, f_(24X), of the eigenmode of the first type; these oscillations are mirror symmetrical only relative to the second imaginary longitudinal section plane, or cause the said deformation body temporarily to appear mirror symmetrical only relative to the second imaginary longitudinal section plane.
 12. The measuring transducer as claimed in claim 10, wherein: the deformation body of said coupling element of the first type is embodied in such a manner, that an eigenfrequency-ratio, inherent to said coupling element, defined by a ratio of the eigenfrequency of its eigenmode of the first type to the eigenfrequency of its eigenmode of second type, is greater than one, especially greater than
 10. 13. The measuring transducer as claimed in claim 8, wherein: the deformation body has at least two longitudinal struts, especially equally constructed and/or plate-shaped longitudinal struts, of which: a first longitudinal strut, which is especially at least sectionally straight, and which extends from said first connecting strut to said third connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane exclusively on a side of said longitudinal section plane occupied both by said first as well as also by said third measuring tube; and a second longitudinal strut, which is especially at least sectionally straight, and which extends from said second connecting strut to said fourth connecting strut, is arranged, spaced apart from the second imaginary longitudinal section plane, for example by the same distance as said first longitudinal strut, exclusively on a side of said longitudinal section plane occupied both by said second as well as also by said fourth measuring tube.
 14. The measuring transducer as claimed in claim 13, wherein: said first longitudinal strut is at least sectionally straight—especially predominantly or completely straight—in projection on the imaginary cross sectional plane; and said second longitudinal strut is at least sectionally straight—for example, predominantly or completely straight—in projection on the imaginary cross sectional plane.
 15. The measuring transducer as claimed in claim 13, wherein: said first longitudinal strut extends at least sectionally perpendicular to the first imaginary longitudinal section plane, and consequently parallel to the second imaginary longitudinal section plane; and said second longitudinal strut extends at least sectionally perpendicular to the first imaginary longitudinal section plane, and consequently parallel to the second imaginary longitudinal section plane.
 16. The measuring transducer as claimed in claim 13, wherein: said first longitudinal strut has a subsection which is straight at least in projection on the imaginary cross sectional plane, wherein this subsection, in projection on said cross sectional plane, extends with a length, extending between said first and said third connecting strut, perpendicular to the first imaginary longitudinal section plane at least in projection on the imaginary cross sectional plane, and extends in a distance, parallel to the second imaginary longitudinal section plane; and said second longitudinal strut has a subsection which is straight at least in projection on the imaginary cross sectional plane, wherein this subsection, in projection on said cross sectional plane, extends with a length, extending between said second and said fourth connecting strut, perpendicular to the first imaginary longitudinal section plane at least in projection on the imaginary cross sectional plane, and extends in a distance, parallel to the second imaginary longitudinal section plane.
 17. The measuring transducer as claimed in claim 16, wherein: the straight subsection of said first longitudinal strut is the same distance from the first imaginary longitudinal section plane as the straight subsection of said second longitudinal strut is, so that the distance, which said first longitudinal strut extends parallel to the second imaginary longitudinal section plane is equal to the distance, which said second longitudinal strut extends parallel to the second imaginary longitudinal section plane; and the straight subsection of said first longitudinal strut is the same length as the straight subsection of said second longitudinal strut, so that the length, with which the straight subsection of said first longitudinal strut extends between said first and said third connecting strut is equal to the length, with which the straight subsection of said second longitudinal strut extends between said first and said third connecting strut.
 18. The measuring transducer as claimed in claim 17, wherein: the entire first longitudinal strut is straight at least in projection on the imaginary cross sectional plane, and in such a manner, that the straight subsection of the first longitudinal strut extends from the first connecting strut up to the third connecting strut, and consequently its length, corresponds to a minimum distance between the first strut end of the first connecting strut and the first strut end of the third connecting strut; and the entire second longitudinal strut is straight at least in projection on the imaginary cross sectional plane, and in such a manner, that the straight subsection of the second longitudinal strut extends from the second connecting strut up to the fourth connecting strut, and consequently its length, corresponds to a minimum distance between the first strut end of the first second connecting strut and the first strut end of the fourth connecting strut.
 19. The measuring transducer as claimed in claim 13, wherein: said first longitudinal strut has a minimal bending stiffness, determined by a modulus of elasticity, dependent on a material of said longitudinal strut, as well as also by a minimum areal moment of inertia, about an imaginary bending principal axis immanent to said longitudinal strut, and said second longitudinal strut has a minimal bending stiffness, determined by a modulus of elasticity, dependent on a material of said longitudinal strut, as well as also by a minimum areal moment of inertia, about an imaginary bending principal axis immanent to said longitudinal strut; and said first longitudinal strut and the second longitudinal strut are arranged in such a manner, that both the imaginary bending principal axis of the minimal areal moment of inertia, of said first longitudinal strut as well as also the imaginary bending principal axis of the minimal areal moment of inertia, of said second longitudinal strut in each case extend parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane.
 20. The measuring transducer as claimed in claim 19, wherein: said first longitudinal strut and said second longitudinal strut are embodied and arranged in such a manner, that the minimal bending stiffness, of said first longitudinal strut is equal to the minimum bending stiffness, of said second longitudinal strut.
 21. The measuring transducer as claimed in claim 19, wherein: said first longitudinal strut has a maximum bending stiffness, determined by the modulus of elasticity, dependant on the material of said longitudinal strut, as well as also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to said longitudinal strut, and said second longitudinal strut has a maximum bending stiffness, determined by the modulus of elasticity, dependent on the material of said longitudinal strut, as well also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to said longitudinal strut; and said first longitudinal strut and said second longitudinal strut are arranged in such a manner, that both the imaginary bending principal axis of the maximal areal moment of inertia, of said first longitudinal strut, as well as also the imaginary bending principal axis of the maximal areal moment of inertia, of said second longitudinal strut, in each case extend parallel to the first imaginary longitudinal section plane and perpendicular to the second imaginary longitudinal section plane.
 22. The measuring transducer as claimed in claim 21, wherein: said first longitudinal strut and said second longitudinal strut are embodied and arranged in such a manner, that the maximum bending stiffness, of said first longitudinal strut is equal to the maximal bending stiffness, of said second longitudinal strut; and/or said first longitudinal strut imaginarily intersects the first imaginary longitudinal section plane, especially with the straight subsection, especially at an angle of 90°; and said second longitudinal strut imaginarily intersects the first imaginary longitudinal section plane, especially with the straight subsection, especially at an angle of 90°.
 23. The measuring transducer as claimed in claim 19, wherein: said first longitudinal strut has a spring stiffness, determined by the modulus of elasticity, dependent on the material of said longitudinal strut, as well as also by said longitudinal strut's strut length, as well as by a surface area, of a cross sectional area coincident with the first imaginary longitudinal section plane, for a tension force or compressive force acting on said longitudinal strut and directed perpendicular to the first imaginary longitudinal section plane, and the second longitudinal strut has a spring stiffness, determined by the modulus of elasticity, dependent on the material of said longitudinal strut, as well as also by the longitudinal strut's strut length, as well as by a surface area, of a cross sectional area coincident with the first imaginary longitudinal section plane, for a tension force or compressive force acting on said longitudinal strut and directed perpendicular to the first imaginary longitudinal section plane.
 24. The measuring transducer as claimed in claim 23, wherein: said first longitudinal strut and said second longitudinal strut are in each case embodied and arranged in such a manner, that the spring stiffness, of said first longitudinal strut is equal to the spring stiffness, of said second longitudinal strut.
 25. The measuring transducer as claimed in claim 23, wherein: said first longitudinal strut and said second longitudinal strut are in each case embodied and arranged in such a manner, that the spring stiffness, behaves proportionally to the relationship E_(L1)·A_(L1)/l_(L1), and the spring stiffness, behaves proportionally to the relationship E_(L2)·A_(L2)/l_(L2).
 26. The measuring transducer as claimed in claim 13, wherein: said first longitudinal strut is formed by means of a flat rod, especially one composed of metal, and said second longitudinal strut is formed by means of a flat rod, especially one composed of metal; and/or said first longitudinal strut and said second longitudinal strut are in each case composed of the same material, and/or in each case composed of steel; and/or said first longitudinal strut and said second longitudinal strut are of equal construction.
 27. The measuring transducer as claimed in claim 13, wherein: said deformation body has a first cross brace, which especially extends from said first longitudinal strut to said second longitudinal strut, and is especially at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane.
 28. The measuring transducer as claimed in claim 27, wherein: said first cross brace has a minimal bending stiffness, determined by a modulus of elasticity, dependent on a material of said cross brace as well as also by a minimum areal moment of inertia, about an imaginary bending principal axis immanent to a said longitudinal strut; and said first cross brace is arranged in such a manner, that the imaginary bending principal axis of its minimal areal moment of inertia, extends parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane, especially in such a manner, that said imaginary bending principal axis lies in the second imaginary longitudinal section plane.
 29. The measuring transducer as claimed in claim 28, wherein: said first cross brace has a maximum bending stiffness, determined by the modulus of elasticity, dependent on the material of said cross brace, as well as also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to said longitudinal strut; and said first cross brace is arranged in such a manner, that said imaginary bending principal axis extends perpendicular to the first imaginary longitudinal section plane and parallel to the second imaginary longitudinal section plane.
 30. The measuring transducer as claimed in claim 27, wherein: said first cross brace of said first connecting strut extends to said second connecting strut; and/or both said first connecting strut as well as also said second connecting strut are affixed with their respective first strut ends on said first cross brace; and/or said first cross brace has a smaller cross section in a region, in which it imaginarily intersects the second imaginary longitudinal section plane, than it has in an adjoining, neighboring region extending to said first connecting strut, than it has in an adjoining, neighboring region extending to said second connecting strut.
 31. The measuring transducer as claimed in claim 27, wherein: said deformation body has a second cross brace, which extends from said first longitudinal strut to said second longitudinal strut, and which especially is at least sectionally straight and/or sectionally non-parallel to the second imaginary longitudinal section plane and/or is constructed equally to said first cross brace.
 32. The measuring transducer as claimed in claim 31, wherein: said second cross brace has an imaginary bending principal axis minimal bending stiffness, determined by a modulus of elasticity, dependent on a material of said cross brace, as well by also of a minimum areal moment of inertia, about an imaginary bending principal axis immanent to said longitudinal strut; and said second cross brace is arranged in such a manner, that said imaginary bending principal axis extends parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane, especially in such a manner, that the imaginary bending principal axis of the minimal areal moment of inertia, of said second cross brace lies in the second imaginary longitudinal section plane.
 33. The measuring transducer as claimed in claim 32, wherein: said second cross brace has a maximum bending stiffness, determined by the modulus of elasticity, dependent on the material of said cross brace, as well as also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to a said longitudinal strut; said second cross brace is arranged in such a manner, that said imaginary bending principal axis extends perpendicular to the first imaginary longitudinal section plane and parallel to the second imaginary longitudinal section plane.
 34. The measuring transducer as claimed in claim 27, wherein: said second cross brace extends from said third connecting strut to said fourth connecting strut; and/or both said third connecting strut as well as also said fourth connecting strut are in each case affixed with their respective first strut ends on said second cross brace; and/or said second cross brace has a smaller cross section in a region, in which it imaginarily intersects the second imaginary longitudinal section plane, than it has in an adjoining, neighboring region extending to said third connecting strut and than it has as in an adjoining neighboring region extending to said fourth connecting strut.
 35. The measuring transducer as claimed in claim 31, wherein: said first cross brace is formed by means of a flat rod, especially one composed of metal, and said second cross brace is formed by means of a flat rod, especially one composed of metal; and/or said first cross brace and said second cross brace are in each case composed of the same material and/or in each case composed of steel.
 36. The measuring transducer as claimed in claim 31, wherein: said deformation body has a third longitudinal strut, which extends from said first cross brace to said second cross brace with a length, which is straight in projection on the imaginary cross sectional plane, and which especially is plate-shaped and/or parallel to the second imaginary longitudinal section plane and/or is in each case spaced apart from the first longitudinal strut by the same distance as said second longitudinal strut.
 37. The measuring transducer as claimed in claim 36, wherein: said third longitudinal strut is affixed with a first strut end on said first cross brace, especially in a region, in which said first cross brace imaginarily intersects the second imaginary longitudinal section plane; and said third longitudinal strut is affixed with a second strut end on said second cross brace, especially in a region, in which said second cross brace imaginarily intersects the second imaginary longitudinal section plane.
 38. The measuring transducer as claimed in claim wherein: said third longitudinal strut is affixed with its first strut end on said first cross brace in the region of its minimum areal moment of inertia, and with its second strut ends on said second cross brace in the region of its minimum areal moment of inertia.
 39. The measuring transducer as claimed in claim 36, wherein: said third longitudinal strut has a minimal bending stiffness, determined by a modulus of elasticity, dependent on a material of said longitudinal strut, as well as by a minimum areal moment of inertia, about an imaginary bending principal axis immanent to said longitudinal strut; and said third longitudinal strut is arranged in such a manner, that said imaginary bending principal axis extends parallel both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane.
 40. The measuring transducer as claimed in claim 36, wherein: said third longitudinal strut has a spring stiffness, determined by the modulus of elasticity, dependent on the material of said longitudinal strut, as well as also by its length, as well as by a surface area, of a cross sectional area coincident with the first imaginary longitudinal section plane, for a tension force or compressive force acting on said longitudinal strut and directed perpendicular to the first imaginary longitudinal section plane.
 41. The measuring transducer as claimed in claim 40, wherein: said third longitudinal strut is embodied and arranged in such a manner, that its spring stiffness, behaves proportionally to a specification E_(L3)·A_(L3)/l_(L3), where E_(L3) is modulus of elasticity A_(L3) is surface area l_(L3) is length
 42. The measuring transducer as claimed in claim 40, wherein: said first, second and third longitudinal struts are embodied in such a manner, that said deformation body fulfills specification: $\frac{{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \frac{E_{L1} \cdot A_{L\; 1}}{l_{L\; 1}}} + {\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}}}{6 \cdot \frac{E_{L\; 1} \cdot J_{{L\; 1},\min}}{l_{L\; 2}}} > 1.$ or specification: $\frac{{\left( \frac{a_{L\; 2}}{2} \right)^{2} \cdot \frac{E_{L\; 2} \cdot A_{L\; 2}}{l_{L\; 2}}} + {\left( \frac{a_{L\; 2}}{2} \right)^{2} \cdot \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}}}{6 \cdot \frac{E_{L\; 2} \cdot J_{{L\; 2},\min}}{l_{L\; 2}}} > 1.$
 43. The measuring transducer as claimed in claim 39, wherein: said third longitudinal strut has a maximum bending stiffness, determined by the modulus of elasticity, dependent on the material of said longitudinal strut, as well as also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to said longitudinal strut; and said third longitudinal strut is arranged in such a manner, that the imaginary bending principal axis of its maximal areal moment of inertia, extends parallel to the first imaginary longitudinal section plane and perpendicular to the second imaginary longitudinal section plane.
 44. The measuring transducer as claimed in claim 36, wherein: said third longitudinal strut is formed by means of a flat rod; and/or said first longitudinal strut, said second longitudinal strut and said third longitudinal strut are each composed of the same material and/or are each composed of steel; and/or the length, of said third longitudinal strut is greater than 10% of the length, of said first longitudinal strut; and/or the length, of said third longitudinal strut is smaller than 120% of the length, of said first longitudinal strut.
 45. The measuring transducer as claimed in claim 9, wherein: each of said connecting struts of said coupling element of the first type is at least sectionally straight, and especially predominantly or completely straight, in projection on the imaginary cross sectional plane.
 46. The measuring transducer as claimed in claim 1, wherein: each of said connecting struts of said coupling element of the first type extends at least sectionally perpendicular to the first imaginary longitudinal section plane, and consequently parallel to the second imaginary longitudinal section plane.
 47. The measuring transducer as claimed in claim 1, wherein: each of said connecting struts of said coupling element of the first type has a straight subsection, which extends perpendicular to the first imaginary longitudinal section plane, and consequently parallel to the second imaginary longitudinal section plane.
 48. The measuring transducer as claimed in claim 47, wherein: each of said connecting struts of said coupling element of the first type imaginarily intersects the first imaginary longitudinal section plane, especially with its respective straight subsection, especially at an angle of 90°.
 49. The measuring transducer as claimed in claim 1, wherein: said first and said third connecting struts are oriented so as to be aligned to one another and wherein said second and fourth connecting struts are oriented so as to be aligned to one another.
 50. The measuring transducer as claimed in claim 1, wherein: said first connecting strut has a maximum bending stiffness, determined by a modulus of elasticity, dependent on a material of said connecting strut, as well as also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to said connecting strut; said second connecting strut has a maximum bending stiffness, determined by a modulus of elasticity, dependent on a material of said connecting strut, as well as also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to said connecting strut; said third connecting strut has a maximum bending stiffness, determined by a modulus of elasticity, dependent on a material of said connecting strut, as well as also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to said connecting strut; and said fourth connecting strut has a maximum bending stiffness, determined by a modulus of elasticity, dependent on a material of said connecting strut, as well as also by a maximal areal moment of inertia, about an imaginary bending principal axis immanent to said connecting strut; and each of said four connecting struts is in each case arranged in such a manner, that the imaginary bending principal axis of their respective maximal areal moments of inertia in each case extends parallel both to the first longitudinal section plane as well as also to the second imaginary longitudinal section plane.
 51. The measuring transducer as claimed in claim 50, wherein: both the maximum areal moment of inertia of said second connecting strut as well as also the maximum areal moment of inertia of said third connecting strut and the maximum areal moment of inertia of said fourth connecting strut are in each case equal to the maximal areal moment of inertia, of said first connecting strut.
 52. The measuring transducer as claimed in claim 50, wherein: said first connecting strut has a minimal bending stiffness, determined by the modulus of elasticity, dependent on the material of said connecting strut, as well as also by a minimum areal moment of inertia, about an imaginary bending principal axis immanent to said connecting strut, said second connecting strut has a minimal bending stiffness, determined by the modulus of elasticity, dependent on the material of said connecting strut, as well as also by a minimum areal moment of inertia, about an imaginary bending principal axis immanent to said connecting strut, said third connecting strut has a minimal bending stiffness, determined by the modulus of elasticity, dependent on the material of said connecting strut, as well as also by a minimum areal moment of inertia, about an imaginary bending principal axis immanent to said connecting strut, and said fourth connecting strut has a minimal bending stiffness, determined by the modulus of elasticity, dependent on the material of said connecting strut, as well as also by a minimum areal moment of inertia, about an imaginary bending principal axis immanent to said connecting strut; and each of said four connecting struts is in each case arranged in such a manner, that the imaginary bending principal axis of their respective minimum areal moments of inertia extends parallel to the first longitudinal section plane and is perpendicular to the second imaginary longitudinal section plane.
 53. The measuring transducer as claimed in claim 50, wherein: the maximum bending stiffness, of said first connecting strut is greater than the minimal bending stiffness, of said first longitudinal strut, especially in such a manner, that the first coupling element fulfills a specification $\frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{E_{L\; 1} \cdot J_{{L\; 1},\max}} > 5.$
 54. The measuring transducer as claimed in claim 1, wherein: each of said—especially equally-constructed—connecting struts is formed by means of a flat rod, which is especially at least sectionally curved in an S-shaped, Z-shaped, V-shaped and/or U-shaped manner in projection on the second imaginary longitudinal section plane; and/or said first connecting strut, said second connecting strut, said third longitudinal strut and said fourth connecting strut are each composed of same material and/or each composed of steel.
 55. The measuring transducer as claimed in claim 9, wherein: said tube arrangement further comprises a second coupling element of a first type, which is spaced apart both from said first flow divider as well as also from said second flow divider, which is affixed on the outlet side to each of said four measuring tubes, which is essentially constructed equally to said first coupling element of said first type, and which serves for adjusting eigenfrequencies of natural oscillation modes of said tube arrangement, especially bending oscillation modes.
 56. The measuring transducer as claimed in claim 55, wherein: both said first coupling element as well as also said second coupling elements of the first type are symmetrical relative to the first imaginary longitudinal section plane of said tube arrangement; and/or both said first coupling element as well as also said second coupling elements of the first type are symmetrical relative to the second imaginary longitudinal section plane of said tube arrangement; and/or said two coupling elements of the first type are arranged symmetrically relative to the imaginary cross sectional plane of said tube arrangement; and/or said coupling elements of the first type are arranged equidistantly relative to the imaginary cross sectional plane of said tube arrangement; and/or both said deformation body of said first coupling element of the first type as well as also said deformation body of the second coupling element of the first type are arranged extending parallel relative to the imaginary cross sectional plane of said tube arrangement; and/or each of said coupling elements of the first type are in each case embodied and arranged in such a manner, that they are mirror symmetrical relative to the first imaginary longitudinal section plane of said tube arrangement; and/or each of said coupling elements of the first type are in each case embodied and arranged in such a manner, that they are mirror symmetrical relative to the second imaginary longitudinal section plane of said tube arrangement.
 57. The measuring transducer as claimed in claim 1, wherein: said tube arrangement further comprises: a first coupling element of a second type, especially a plate-shaped first coupling element of a second type, which, for forming inlet-side oscillation nodes both for vibrations—especially bending oscillations—of said first measuring tube, as well as also for vibrations—especially bending oscillations—of said second measuring tube opposite-equal thereto, is affixed on the inlet side to said first measuring tube and to said second measuring tube; a second coupling element of the second type, which is especially plate-shaped and/or constructed equally to said first coupling element of the second type and/or parallel to said first coupling element of the second type, and which, for forming outlet-side oscillation nodes both for vibrations—especially bending oscillations—of said first measuring tube, as well as also for vibrations—especially bending oscillations—of said second measuring tube opposite-equal thereto, is affixed on the outlet side to said first measuring tube and to said second measuring tube; a third coupling element of the second type, which is especially plate shaped and/or constructed equally to said first coupling element of the second type and/or parallel to said second coupling element of the second type, and which, for forming inlet-side oscillation nodes both for vibrations—especially bending oscillations—of said third measuring tube, as well as also for vibrations—especially bending oscillations—of said fourth measuring tube opposite-equal thereto, is affixed the inlet side, spaced apart both from said first flow divider as well as also from said second flow divider, to said third measuring tube and to said fourth measuring tube; as well as a fourth coupling element of the second type, which is especially plate-shaped and/or constructed equally to said first coupling element of the second type and/or parallel to said first coupling element of the second type, and which, for forming outlet-side oscillation nodes both for vibrations—especially bending oscillations—of said third measuring tube, as well as also for vibrations—especially bending oscillations—of said fourth measuring tube opposite-equal thereto, is affixed on the outlet side, spaced apart both from said first flow divider as well as also from said second flow divider, as well as also from said first coupling element, to said third measuring tube and to said fourth measuring tube.
 58. The measuring transducer as claimed in claim 57, wherein: said first coupling element of the second type is affixed both on a tube segment of said first measuring tube extending between said first flow divider and said first coupling element of the first type, as well as also on a tube segment of said second measuring tube extending between said first flow divider and said first coupling element of the first type, and said second coupling element of the second type is affixed both on a tube segment of said first measuring tube extending between said second flow divider and said second coupling element of the first type, as well as also on a tube segment of said second measuring tube extending between said second flow divider and the second coupling element of the first type, in such a manner, that a wanted oscillatory length of said second measuring tube corresponding to a length of a section of a deflection curve of said second measuring tube extending between said first coupling element of the second type and said second coupling element of the second type is equal to a wanted oscillatory length, of said first measuring tube corresponding to a length of a section of a deflection curve of said first measuring tube extending between said first coupling element of the second type and the second coupling element of the second type, and that a minimal distance between said first coupling element of the second type and the second end of said second connecting strut of the coupling element of the first type, measured along a surface element of said second measuring tube, is equal to a minimum distance, between said first coupling element of the second type and the second end of said first connecting strut of the coupling element of said first type, measured along a surface element of the first measuring tube; and said third coupling element of the second type is affixed both on a first type tube segment of said third measuring tube extending between said first flow divider and said first coupling element as well as also on a tube segment of said fourth measuring tube extending between said first flow divider and said first coupling element of the first type, and said fourth coupling element of the second type is affixed both on a tube segment of said third measuring tube extending between said second flow divider and said second coupling element of first type as well as also on a tube segment of said fourth measuring tube extending between said second flow divider and said second coupling element of the first type, in such a manner, that both a wanted oscillatory length of said third measuring tube corresponding to a length of a section of a deflection curve of said third measuring tube extending between said third coupling element of the second type and said fourth coupling element of the second type, as well as also a wanted oscillatory length of said fourth measuring tube corresponding to a length of a section of a deflection curve of said fourth measuring tube extending between said third coupling element of the second type and said fourth coupling element of the second type are in each case equal to the wanted oscillatory length, of said first measuring tube, and that both a minimal distance between said third coupling element of the second type and the second end of said third connecting strut of the coupling element of the first type, measured along a surface element of said third measuring tube, as well as also minimal distance between said third coupling element of the second type and the second end of said fourth connecting strut of the coupling element of said first type, measured along a surface element of the fourth measuring tube, are in each case equal to the minimum distance, between said first coupling element of the second type and the second end of said first connecting strut of the coupling element of the first type.
 59. The measuring transducer as claimed in claim 57, wherein: the wanted-oscillatory length, of said first measuring tube amounts to less than 3000 mm, especially less than 2500 mm and/or more than 800 mm; and/or a caliber-to-oscillatory length-ratio, of the measuring transducer, defined by a ratio of a caliber, of said first measuring tube to the wanted oscillatory length, of said first measuring tube, amounts to more than 0.03, especially more than 0.05 and/or less than 0.15.
 60. The measuring transducer as claimed in claim 1, wherein: each of said four measuring tubes—which are especially of an equal size—has a caliber, which amounts to more than 40 mm, especially more than 60 mm.
 61. The measuring transducer as claimed in claim wherein: each of said four measuring tubes in each case has a tube cross section determined by a caliber of said measuring tube as well as a wall thickness of said measuring tube; and both said second measuring tube as well as also said third measuring tube and said fourth measuring tube in each case has a caliber, which in each case is equal to a caliber, of said first measuring tube, and in each case has a wall thickness, which is equal to a wall thickness, of said first measuring tube, and, consequently, both said second measuring tube as well as also said third measuring tube and said fourth measuring tube in each case have an outer diameter which is equal to an outer diameter, of said first measuring tube.
 62. The measuring transducer as claimed in claim 61, wherein: the distance, of said first longitudinal strut to the second imaginary longitudinal section plane amounts to less than 200% of said outer diameter, and more than 50% of said outer diameter.
 63. The measuring transducer as claimed in claim 1, wherein: each of said four connecting struts in each case has a strut length defined by a minimum distance between its respective first strut end and its respective second strut end; and both said second connecting strut as well as also said third as well as said fourth connecting strut in each case have a strut length, which, in each case, is equal to the strut length, of said first connecting strut.
 64. The measuring transducer as claimed in claim 61, wherein: the tube arrangement fulfills both the specification: ${\frac{l_{V\; 1}}{l_{V\; 1} + {0.5 \cdot l_{L\; 1}}} > 0.3},$ as well as also the specification: $\frac{l_{V\; 1}}{l_{V\; 1} + {0.5 \cdot l_{L\; 1}}} < {0.7.}$
 65. The measuring transducer as claimed in claim 1, wherein: the tube arrangement fulfills the specification: $\frac{\frac{E_{V\; 1} \cdot A_{V\; 1}}{l_{V\; 1}}}{3 \cdot \frac{E_{18} \cdot J_{18}}{a_{K}^{3} \cdot \left( {1 - {1.5 \cdot \frac{a_{k}}{L_{18x}}}} \right)}} < 20.$
 66. The measuring transducer as claimed in claim 3, wherein: said measuring tubes are bent in such a manner and arranged in such a manner, that a caliber-to-height-ratio, of the tube arrangement, defined by a ratio of the caliber, of said first measuring tube to a maximal lateral expansion, of the tube arrangement, measured from a peak of said first measuring tube to a peak of said third measuring tube, amounts to more than 0.05, especially more than 0.07, and/or less than 0.35, especially less than 0.2.
 67. The measuring transducer as claimed in claim 66, wherein: the tube arrangement fulfills both the specification: $\frac{l_{V\; 1} + {0.5 \cdot l_{L\; 1}}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} > 0.2$ as well as also the specification ${\frac{l_{V\; 1} + {0.5 \cdot l_{L\; 1}}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} < 0.9};$ and/or wherein the tube arrangement fulfills both the specification: $\frac{0.5 \cdot l_{L\; 1}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} > 0.1$ as well as also the specification: $\frac{0.5 \cdot l_{L\; 1}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} < {0.5.}$
 68. The measuring transducer as claimed in claim 67, wherein: the tube arrangement has between said first measuring tube and said third measuring tube a minimum distance, especially determined by a minimum distance between the first and third flow opening of said first flow divider, or the first and third flow opening of said second flow divider; and the tube arrangement fulfills the specification: $\frac{0.5 \cdot l_{L\; 1}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} \leq {\frac{a_{k}}{L_{18,x}} + {\frac{{0.5 \cdot D_{18}} + h_{18} + {0.5 \cdot A_{18}}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)}.}}$
 69. The measuring transducer as claimed in claim 68, wherein: the tube arrangement fulfills the specification: $\frac{0.5 \cdot l_{L\; 1}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)} > {{0.2\frac{a_{k}}{L_{18,x}}} + {\frac{{0.5 \cdot D_{18}} + h_{18} + A_{18}}{{0.5 \cdot Q_{18}} - \left( {D_{18} + {2 \cdot h_{18}}} \right)}.}}$
 70. The measuring transducer as claimed in claim 1, wherein: said four measuring tubes, said first coupling element of the first type, as well as said first, second, third and fourth coupling elements of the second type are embodied and arranged in such a manner, that, as a result, the tube arrangement fulfills the specification $\frac{\frac{1}{l_{V\; 1}^{2}} \cdot \left\lbrack {\frac{1}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} + \frac{1}{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \left( {\frac{E_{L\; 1} \cdot A_{L\; 1}}{l_{L\; 1}} + \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}} \right)}} \right\rbrack}{3 \cdot \frac{E_{18} \cdot J_{18}}{a_{K}^{3} \cdot \left( {1 - {1.5 \cdot \frac{a_{k}}{L_{18x}}}} \right)}} > {0.01.}$
 71. The measuring transducer as claimed in claim 1, wherein: said first coupling element of the first type fulfills the specification ${\frac{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \left( {\frac{E_{L\; 1} \cdot A_{L\; 1}}{l_{L\; 1}} + \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}} \right)}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} > 2};$ and/or said first coupling element of the first type fulfills the specification $\frac{\frac{1}{l_{V\; 1}^{2}} \cdot \left\lbrack {\frac{1}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} + \frac{1}{\left( \frac{a_{L\; 1}}{2} \right)^{2} \cdot \left( {\frac{E_{L\; 1} \cdot A_{L\; 1}}{l_{L\; 1}} + \frac{E_{L\; 3} \cdot A_{L\; 3}}{l_{L\; 3}}} \right)}} \right\rbrack}{\frac{1}{l_{V\; 1}^{2}} \cdot \left\lbrack {\frac{1}{3 \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\max}}{l_{V\; 1}}} + \frac{1}{6 \cdot \frac{E_{L\; 1} \cdot J_{{L\; 1},\min}}{l_{L\; 1}}}} \right\rbrack} > 1.$
 72. The measuring transducer as claimed in claim 1, wherein: the tube arrangement has a natural bending oscillation mode of a first type, in which said first measuring tube and said second measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane, especially bending oscillations which are symmetric relative to the second imaginary longitudinal section plane, in each case about a static rest position associated with the respective measuring tube, especially cantilever, bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes, and in which said third measuring tube and said fourth measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane, especially bending oscillations which are symmetric relative to the second imaginary longitudinal section plane, in each case about a static rest position associated with the respective measuring tube, especially cantilever, bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes, in such a manner, that, relative to the second imaginary longitudinal section plane, said bending oscillations of said first measuring tube are also opposite-equal to said bending oscillations of said third measuring tube, and that, relative to the second imaginary longitudinal section plane, said bending oscillations of said second measuring tube are also opposite-equal to said bending oscillations of said fourth measuring tube.
 73. The measuring transducer as claimed in claim 72, wherein: the tube arrangement has a natural bending oscillation mode of a second type (X-mode), in which said first measuring tube and said second measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane, especially bending oscillations which are symmetric relative to the second imaginary longitudinal section plane, in each case about a static rest position associated with the respective measuring tube, especially cantilever, bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes, and in which said third measuring tube and said fourth measuring tube execute bending oscillations which are opposite-equal relative to the second imaginary longitudinal section plane, especially bending oscillations which are symmetric relative to the second imaginary longitudinal section plane, in each case about a static rest position associated with the respective measuring tube, especially cantilever, bending oscillations in each case about an imaginary oscillation axis parallel to at least two of the imaginary connecting axes, in such a manner, that, relative to the second imaginary longitudinal section plane, said bending oscillations of said first measuring tube are also opposite-equal to said bending oscillations of said fourth measuring tube, and that, relative to the second imaginary longitudinal section plane, said bending oscillations of said second measuring tube are also opposite-equal to said bending oscillations of said third measuring tube.
 74. The measuring transducer as claimed in claim 73, wherein: an eigenfrequency, of the bending oscillation mode of the first type, measurable in the case of measuring tubes filled completely with air as a reference medium, is different from an eigenfrequency, of the bending oscillation mode of the second type measurable at the same time as said eigenfrequency, of the bending oscillation mode of the first type and/or measurable in the case of measuring tubes completely filled with said reference medium, especially by more than 10 Hz, especially in such a manner, that said eigenfrequency, of the bending oscillation mode of the first type is more than 10 Hz smaller than said eigenfrequency, of the bending oscillation mode of the second type, and/or that said eigenfrequency, of the bending oscillation mode of the first type amounts to less than 99%, especially less than 95%, of said eigenfrequency, of the bending oscillation mode of the second type.
 75. The measuring transducer as claimed in claim 72, wherein: said exciter mechanism is embodied in such a manner, that the bending oscillation mode of the first type is excitable therewith.
 76. The measuring transducer as claimed in claim 73, wherein: said exciter mechanism is embodied in such a manner, that the bending oscillation mode of the second type is excitable therewith, especially simultaneously to the bending oscillation mode of the first type.
 77. The measuring transducer as claimed in claim 1, wherein: said second measuring tube, said third measuring tube and said fourth measuring tube each have an empty mass, which is equal to an empty mass, of said first measuring tube is; and/or said first measuring tube has an empty mass, which is greater than 20 kg, especially greater than 30 kg and/or smaller than 50 kg.
 78. The measuring transducer as claimed in claim 77, wherein: said deformation body of the coupling element of the first type has a mass, which amounts to less than 50% of the empty mass, of said first measuring tube.
 79. The measuring transducer as claimed in claim 78, wherein: an empty mass, of said deformation body of said first coupling element of the first type is more than 10% of the empty mass, of said first measuring tube; and/or said first coupling element of the first type fulfills the specification: $\sqrt{\frac{\frac{1}{M_{VK}} \cdot \frac{E_{V\; 1} \cdot J_{{V\; 1},\min}}{l_{V\; 1}^{3}}}{f_{{18V},{Ref}}}} > {1.05.}$
 80. The measuring transducer as claimed in claim 11, wherein: inherent to the coupling element of the first type is a natural oscillatory mode of a third type, in which said deformation body, for example, only moving translationally in the direction of a longitudinal axis parallel both to the first imaginary longitudinal section plane as well as also to the second imaginary longitudinal section plane, can oscillate with an eigenfrequency, about an associated static rest position, and in such a manner, that simultaneous to this, said four connecting struts execute—especially in the same direction and/or uniformly—bending oscillations about a particular static resting position, in the direction of the longitudinal axis.
 81. The measuring transducer as claimed in claim 80, wherein: the coupling element of the first type is embodied in such a manner, that the eigenfrequency, of its eigenmode of the third type is not equal to the eigenfrequency, of the bending oscillation mode of the first type of said tube arrangement measurable in the case of measuring tubes completely filled with air, especially in such a manner, that said eigenfrequency, of the oscillatory mode of the third type of the coupling element of the first type is more than 10 Hz greater than said eigenfrequency, of the bending oscillation mode of the first type of said tube arrangement, and/or that said eigenfrequency, of the oscillatory mode of the third type of the coupling element of the first type amounts to more than 101%, especially more than 105%, of said eigenfrequency, of the bending oscillation mode of said first type the tube arrangement.
 82. The measuring transducer as claimed in claim 81, wherein: inherent to the coupling element of the first type is a natural oscillatory mode of a fourth type, in which said deformation body, moving only translationally in the plane of oscillation parallel to the imaginary cross sectional plane, can oscillate about its associated static rest position with an eigenfrequency, in such a manner, that said four connecting struts especially execute—uniformly and/or in the same direction—bending oscillations about their respective static resting positions in the coupler plane; and said coupling element of the first type is embodied in such a manner, that the eigenfrequency, of its eigenmode of the fourth type is higher than the eigenfrequency, of the bending oscillation mode of the second type of said tube arrangement, especially in such a manner, that said eigenfrequency, of the mode of oscillation of the fourth type of said coupling element of the first type is more than 10 Hz greater than said eigenfrequency, of the bending oscillation mode of the second type of said tube arrangement, and/or that said eigenfrequency, of the mode of oscillation of the fourth type of said coupling element of the first type amounts to more than 101%, especially more than 105%, of said eigenfrequency, of the bending oscillation mode of the second type of said tube arrangement.
 83. The measuring transducer as claimed in claim wherein: a measuring tube length, of said first measuring tube corresponding to a length of a section of a deflection curve of said first measuring tube extending between said first flow opening of said first flow divider and said first flow opening of said second flow divider amounts to more than 1000 mm, especially more than 1200 mm and/or less than 3000 mm, especially less than 2500 mm.
 84. The measuring transducer as claimed in claim 1, wherein: said two flow dividers are embodied and arranged in the measuring transducer in such a manner, that a first imaginary longitudinal section plane of the measuring transducer, within which the first imaginary connecting axis and the second imaginary connecting axis—which are especially parallel to a principal flow axis of the measuring transducer aligning with the pipeline—extend, is parallel to a second imaginary longitudinal section plane of the measuring transducer, within which the imaginary third connecting axis and the imaginary fourth connecting axis extend; especially in such a manner, that the first imaginary longitudinal section plane of the tube arrangement lies between the first and second imaginary longitudinal section planes of the measuring transducer, and/or is parallel to the first and second imaginary longitudinal section planes of the measuring transducer.
 85. The measuring transducer as claimed in claim 84, wherein: said two flow dividers are embodied and arranged in the measuring transducer in such a manner, that a third imaginary longitudinal section plane of the measuring transducer, within which the imaginary first connecting axis and the imaginary third connecting axis extend, is parallel to a fourth imaginary longitudinal section plane of the measuring transducer, within which the imaginary second connecting axis and the imaginary fourth connecting axis extend.
 86. The measuring transducer as claimed in claim 85, wherein: said measuring tubes are embodied and arranged in the measuring transducer in such a manner, that the second imaginary longitudinal section plane of said tube arrangement extends between the third imaginary longitudinal section plane of the measuring transducer and the fourth imaginary longitudinal section plane of the measuring transducer, especially in such a manner, that the second imaginary longitudinal section plane of said tube arrangement is parallel to the third imaginary longitudinal section plane of the measuring transducer and parallel to the fourth imaginary longitudinal section plane of the measuring transducer.
 87. The measuring system as claimed in claim 1, wherein: each of said four measuring tubes has a measuring tube peak, defined as the greatest perpendicular distance of the respective measuring tube from the first imaginary longitudinal section plane.
 88. The measuring transducer as claimed in claim 1, wherein: said first measuring tube has a caliber, which is equal to a caliber of said second measuring tube, and especially also equal to a caliber of said third measuring tube as well as equal to a caliber of said fourth measuring tube; and/or said four measuring tubes are of equal construction as regards material of their tube walls, and/or as regards their geometric tube dimensions, especially a measuring tube length, a tube wall thickness, a tube outer diameter and/or a caliber; and/or a material of the tube walls of said four measuring tubes is at least partially composed of titanium and/or zirconium and/or stainless steel and/or duplex steel and/or super duplex steel; and/or said transducer housing, said flow dividers and tube walls of said measuring tubes are each composed of steel, especially stainless and/or high strength steel.
 89. The measuring transducer as claimed in claim 1, wherein: said first flow divider has a flange for connecting the measuring transducer to a tube segment of the pipeline serving for supplying medium to the measuring transducer, and said second flow divider has a flange for connecting the measuring transducer to a tube segment of the pipeline serving for removing medium from the measuring transducer.
 90. The measuring transducer as claimed in claim 1, wherein: a middle segment of said transducer housing is formed at least partially by means of a straight, especially circularly cylindrical, support tube, especially in such a manner, that a segment of said first measuring tube extending on a first side outwards from said support tube and a segment of said second measuring tube extending on the first side outwards from said support tube are surrounded by a first housing cap of said transducer housing, and that a segment of said third measuring tube extending on a second side (lying opposite to the first side) outwards from said support tube and a segment of said fourth measuring tube extending on the second side outwards from said support tube are surrounded by a second housing cap of said transducer housing, especially a second housing cap constructed equally to said first housing cap.
 91. The measuring transducer as claimed in claim 89, wherein: each of said flanges has a sealing surface for fluid-tight connecting of the measuring transducer with the corresponding tube segment of the pipeline; and a distance between said sealing surfaces of said two flanges defines an installed length, of the measuring transducer, especially an installed length amounting to more than 1200 mm and/or less than 3000 mm, especially less than 2500 mm.
 92. The measuring transducer as claimed in claim 91, wherein: a measuring-tube-length-to-installed length-ratio, of the measuring transducer, defined by a ratio of the measuring tube length, of said first measuring tube to the installed length, of the measuring transducer, amounts to more than 0.7, especially more than 0.8 and/or less than 1.2.
 93. The measuring transducer as claimed in claim 1, further comprising: a sensor arrangement reacting to vibrations of said measuring tubes, especially bending oscillations excited by means of said exciter mechanism—especially an electro-dynamic sensor arrangement and/or a sensor arrangement formed by means of oscillation sensors constructed equally to one another—for producing oscillation signals representing vibrations, especially bending oscillations, of said measuring tubes.
 94. The measuring transducer as claimed in claim 93, wherein: said sensor arrangement is formed by means of an inlet-side first oscillation sensor, especially an electrodynamic inlet-side first oscillation sensor and/or an inlet-side first oscillation sensor differentially registering oscillations of the first measuring tube relative to said second measuring tube, as well as by means of an outlet-side second oscillation sensor, especially an electrodynamic outlet-side second oscillation sensor and/or an outlet-side second oscillation sensor differentially registering oscillations of the first measuring tube relative to said second measuring tube.
 95. The measuring transducer as claimed in claim 94, wherein: said sensor arrangement is formed by means of an inlet-side third oscillation sensor, especially an electrodynamic inlet-side third oscillation sensor and/or an inlet-side third oscillation sensor differentially registering oscillations of said third measuring tube relative to said fourth measuring tube and/or one electrically connected in series with the first oscillation sensor, as well as by means of an outlet-side fourth oscillation sensor, especially an electrodynamic outlet-side fourth oscillation sensor and/or an electrodynamic outlet-side fourth oscillation sensor differentially registering oscillations of said third measuring tube relative to said fourth measuring tube and/or one electrically connected in series with the second oscillation sensor.
 96. A measuring system for measuring density and/or mass flow rate—especially also a total mass flow totalled over a time interval—of a medium, especially a gas, a liquid, a powder or other flowable material, flowing, at least at times, in a pipeline, especially with a mass flow rate of more than 1000 t/h, especially a measuring system embodied as an In-line measuring device and/or as a measuring device in compact construction, comprising: a measuring transducer as claimed in claim 1; and transmitter electronics electrically coupled with the measuring transducer—especially a transmitter electronics arranged in an electronics housing mechanically connected with the transducer housing—for activating the measuring transducer, especially its exciter mechanism, and for evaluating oscillation signals delivered by the measuring transducer.
 97. The measuring system as claimed in claim 96, wherein: during operation, said four measuring tubes, excited by said exciter mechanism, simultaneously execute bending oscillations, especially bending oscillations in a bending oscillation fundamental mode of first type.
 98. The measuring system as claimed in claim 96, wherein: said exciter mechanism comprises at least a first oscillation exciter acting—especially differentially—on the first and second measuring tubes, especially a first oscillation exciter affixed to said first and second measuring tubes and/or an electro-dynamic first oscillation exciter, for converting electrical excitation power into said exciter mechanism fed by means of said transmitter electronics into mechanical exciter forces effecting bending oscillations of said first measuring tube, especially variable and/or periodic bending oscillations having at least one signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of said tube arrangement, and effecting bending oscillations of said second measuring tube opposite-equal to said bending oscillations of said first measuring tube relative to the second imaginary longitudinal section plane of said tube arrangement.
 99. The measuring system as claimed in claim 98, wherein: said first oscillation exciter is formed by means of a permanent magnet held on said first measuring tube, especially a permanent magnet held on said first measuring tube in the region of a measuring tube peak, and a cylindrical coil held on said second measuring tube, especially a cylindrical coil held on said second measuring tube in the region of a measuring tube peak, and permeated by the magnetic field of the permanent magnet.
 100. The measuring system as claimed in claim 98, wherein: said exciter mechanism further comprises a second oscillation exciter acting—especially differentially—on said third and fourth measuring tubes, especially a second oscillation exciter affixed to said third and fourth measuring tubes, and/or an electro-dynamic second oscillation exciter and/or one constructed equally to said first oscillation exciter and/or one electrically connected in series with said first oscillation exciter, for converting electrical excitation power into said exciter mechanism fed by means of said transmitter electronics into mechanical exciter forces effecting variable and/or periodic bending oscillations of said third measuring tube, especially bending oscillations with at least one signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of said tube arrangement, and effecting bending oscillations of said fourth measuring tube opposite-equal to said bending oscillations of said third measuring tube relative to the second imaginary longitudinal section plane of said tube arrangement.
 101. The measuring system as claimed in claim 100, wherein: said second oscillation exciter is formed by means of a permanent magnet held on said third measuring tube, especially a permanent magnet held on said third measuring tube in the region of a measuring tube peak, and by means of a cylindrical coil held on said fourth measuring tube, especially a cylindrical coil held on said fourth measuring tube in the region of a measuring tube peak, and permeated by the magnetic field of the respective permanent magnet.
 102. The measuring system as claimed in claim 96, wherein: said transmitter electronics feeds electrical excitation power into said exciter mechanism by means of at least one variable and/or at least at times periodic, electrical driver signal supplied to said exciter mechanism, especially a driver signal having at least one signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of said tube arrangement, especially a driver signal having a variable maximal voltage level and/or a variable maximal electrical current level; and said exciter mechanism converts the electrical excitation power, especially electrical excitation power dependent on a voltage level and an electrical current level of the at least one driver signal, at least partially both into bending oscillations of said first measuring tube and into bending oscillations of said second measuring tube opposite-equal to bending oscillations of said first measuring tube relative to the second imaginary longitudinal section plane of said tube arrangement, as well as also into bending oscillations of said third measuring tube and into bending oscillations of said fourth measuring tube opposite-equal to bending oscillations of said third measuring tube relative to the second imaginary longitudinal section plane of said tube arrangement.
 103. The measuring system as claimed in claim 94, wherein: the at least one driver signal is fed to said first oscillation exciter, especially in such a manner, that a first exciter current flows through its cylindrical coil, driven by a variable first exciter voltage provided by means of said first driver signal.
 104. The measuring system as claimed in claim 102, wherein: said at least one driver signal has a plurality of signal components with signal frequencies differing from one another; and at least one of the signal components (especially a signal component dominating as regards to signal power) of said first driver signal has a signal frequency corresponding to an eigenfrequency of a natural mode of oscillation of said tube arrangement, especially of the bending oscillation mode of first type, in which each of said four measuring tubes executes bending oscillations.
 105. The measuring system as claimed in claim 98, wherein: said exciter mechanism effects oscillations of said measuring tubes, especially bending oscillations in the first bending oscillation mode of first type, by the fact that an exciter force generated by means of said first oscillation exciter and acting on said first measuring tube is opposite, especially opposite-equal, to an exciter force generated at the same time by means of said first oscillation exciter and acting on said second measuring tube.
 106. The measuring system as claimed in claim 96, wherein: said transmitter electronics, based on electrical excitation power converted in said exciter mechanism, generates a viscosity measured value representing viscosity of the flowing medium; and/or said transmitter electronics, based on oscillation signals delivered by the measuring transducer, generates a mass flow measured value representing a mass flow rate of the flowing medium and/or a density measured value representing density of the flowing medium.
 107. The use of a measuring transducer as claimed in claim 1, for measuring density and/or mass flow rate, especially also total mass flow totalled over a time interval, and/or viscosity and/or Reynolds number of a medium, especially a gas, liquid, powder or other flowable material flowing in a process line, especially a pipeline, at least at times with a mass flow rate of more than 1000 t/h, especially more than 1500 t/h. 